BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Bruno Amorim (Universidade do Minho) DTSTART:20200513T100000Z DTEND:20200513T110000Z DTSTAMP:20260404T094545Z UID:QM3/1 DESCRIPTION:Title: Strain in two-dimensional materials\nby Bruno Amorim (Universidade do Minho) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstra ct\nGraphene is the prototypical two-dimensional material. One of main fea tures of two-dimensional materials is the ease with which their properties can be externally modified. Application of strain is one possible way. In this seminar we will review the geometrical description of strains in cry stalline materials\, with a focus on graphene. Using this method\, we will study the form of the electron-lattice interaction. We will compare this model with the description of electrons in strained graphene in terms of a Dirac equation in curved space. An overview of anharmonic lattice effects in two-dimensional materials will also be made.\n LOCATION:https://stable.researchseminars.org/talk/QM3/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Joe Huxford (Oxford University) DTSTART:20200520T100000Z DTEND:20200520T110000Z DTSTAMP:20260404T094545Z UID:QM3/2 DESCRIPTION:Title: Topological phases in 3+1D: the higher lattice gauge theory model and i ts excitations\nby Joe Huxford (Oxford University) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nTopological phases in 3+1 D are less well understood than\ntheir lower dimensional counterparts. A u seful approach to the study\nof such phases is to look at toy models that we can solve exactly. In\nthis talk I will present new results for an exis ting model for certain\ntopological phases in 3+1D (the model was first pr esented in [1]).\nThis model is based on a generalisation of lattice gauge theory known\nas higher lattice gauge theory\, which treats parallel tran sport of\nlines as well as points. I will first provide a brief introducti on to\nhigher lattice gauge theory and the Hamiltonian model constructed f rom\nit. Then we will look at the simple excitations (both point-like and\ nloop-like) that are present in this model and how these excitations\ncan be constructed explicitly using so-called ribbon and membrane\noperators. Some of the quasi-particles are confined and we discuss how\nthis arises f rom a condensation-confinement transition. We will then\nlook at the (loop -)braiding relations of the excitations and finish by\nexamining the conse rved topological charges realised by the Higher\nLattice Gauge Theory Mode l.
\n\n[1] A Bullivant\, M. Calcada et al.\, ``Topological phases from higher\ngauge symmetry in 3+1D"\, Phys. Rev. B 95\, 155118 (2017)\n LOCATION:https://stable.researchseminars.org/talk/QM3/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Achilleas Lazarides (Loughborough University) DTSTART:20200527T100000Z DTEND:20200527T110000Z DTSTAMP:20260404T094545Z UID:QM3/3 DESCRIPTION:Title: Quantum order at infinite temperature\, time crystals\, and dissipation \nby Achilleas Lazarides (Loughborough University) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nDiscrete time crystals is the name given to many-body systems displaying long-time dynamics that is sub-harmonic with respect to a driving frequency. While these were first discussed in closed quantum systems a few years ago\, recent work (partly motivated by experiments) has focussed on including non-unitary effects su ch as due to an external environment ("dissipation").\n\nIn this talk I wi ll begin by discussing general features of periodically-driven many-body s ystems\, then concentrate on one of the unitary models for discrete time c rystals. Time permitting\, I will finally I will discuss a general framewo rk for subharmonic oscillations stabilised by dissipative dynamics.\n LOCATION:https://stable.researchseminars.org/talk/QM3/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Johanna Erdmenger (University of Würzburg) DTSTART:20200603T100000Z DTEND:20200603T110000Z DTSTAMP:20260404T094545Z UID:QM3/4 DESCRIPTION:Title: Turbulent hydrodynamics in strongly correlated Kagome metals\nby Jo hanna Erdmenger (University of Würzburg) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nA current challenge in condensed matte r physics is the realization of strongly correlated\, viscous electron flu ids. These fluids are not amenable to the perturbative methods of Fermi li quid theory\, but can be described by holography\, that is\, by mapping th em onto a weakly curved gravitational theory via gauge/gravity duality. Th e canonical system considered for realizations has been graphene\, which p ossesses Dirac dispersions at low energies as well as significant Coulomb interactions between the electrons. In this work\, we show that Kagome sys tems with electron fillings adjusted to the Dirac nodes of their band stru cture provide a much more compelling platform for realizations of viscous electron fluids\, including non-linear effects such as turbulence. In part icular\, we find that in stoichiometric Scandium (Sc) Herbertsmithite\, th e fine-structure constant\, which measures the effective Coulomb interacti on and hence reflects the strength of the correlations\, is enhanced by a factor of about 3.2 as compared to graphene\, due to orbital hybridization . We employ holography to estimate the ratio of the shear viscosity over t he entropy density in Sc-Herbertsmithite\, and find it about three times s maller than in graphene. These findings put\, for the first time\, the tur bulent flow regime described by holography within the reach of experiments .\n LOCATION:https://stable.researchseminars.org/talk/QM3/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Zlatko Papic (University of Leeds) DTSTART:20200610T100000Z DTEND:20200610T110000Z DTSTAMP:20260404T094545Z UID:QM3/5 DESCRIPTION:Title: Quantum many-body scars: a new form of weak ergodicity breaking in cons trained quantum systems\nby Zlatko Papic (University of Leeds) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nRecent experi ments on large chains of Rydberg atoms [1] have demonstrated the possibili ty of realising one-dimensional\, kinetically constrained quantum systems. It was found that such systems exhibit surprising signatures of non-ergod ic dynamics\, such as robust periodic revivals in global quenches from cer tain initial states. This weak form of ergodicity breaking has been interp reted as a manifestation of "quantum many-body scars" [2]\, i.e.\, the man y-body analogue of unstable classical periodic orbits of a single particle in a chaotic stadium billiard. Scarred many-body eigenstates have been sh own to exhibit a range of unusual properties which violate the Eigenstate Thermalisation Hypothesis\, such as equidistant energy separation\, anomal ous expectation values of local observables and subthermal entanglement en tropy. I will demonstrate that these properties can be understood using a tractable model based on a single particle hopping on the Hilbert space gr aph\, which formally captures the idea that scarred eigenstates form a rep resentation of a large spin that is embedded in a thermalising many-body system. I will show that this picture allows to construct a more general f amily of scarred models where the fundamental degree of freedom is a quant um clock [3]. These results suggest that scarred many-body bands give rise to a new universality class of constrained quantum dynamics\, which opens up opportunities for creating and manipulating novel states with long-liv ed coherence in systems that are now amenable to experimental study.
\n \n[1] H. Bernien et al.\, Nature 551\, 579 (2017).
\n[2] C. J. Turner\, A. A. Michailidis\, D. A. Abanin\, M. Serbyn\, Z. Papic\, Nat. Phys. 14\, 745 (2018).
\n[3] Kieran Bull\, Ivar Martin\, and Z. Papic\, Phys. Rev . Lett. 123\, 030601 (2019).\n LOCATION:https://stable.researchseminars.org/talk/QM3/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Mário Silveirinha (Instituto Superior Técnico) DTSTART:20200624T100000Z DTEND:20200624T110000Z DTSTAMP:20260404T094545Z UID:QM3/6 DESCRIPTION:Title: Topological theory of non-Hermitian photonic systems\nby Mário Sil veirinha (Instituto Superior Técnico) as part of Quantum Matter meets Mat hs (IST\, Lisbon)\n\n\nAbstract\nRecently\, topological materials and topo logical effects have elicited a great interest in the photonics community [1]. While condensed-matter phenomena are traditionally described by Herm itian operators\, the same is not true in the context of macroscopic elect rodynamics where a dissipative response is the rule\, not the exception. I n this talk\, I will discuss how to determine the topological phases of di ssipative (non-Hermitian) photonic structures from first principles using a gauge-independent Green function [2\, 3]. It is shown that analogous to the Hermitian case\, the Chern number can be expressed as an integral of t he system Green function over a line parallel to the imaginary-frequency a xis. The approach introduces in a natural way the "band-gaps" of non-Hermi tian systems as the strips of the complex-frequency plane wherein the syst em Green function is analytical. I apply the developed theory to nonrecipr ocal electromagnetic continua and photonic crystals\, with lossy and or ga iny elements. Furthermore\, I discuss the validity of the bulk-edge corres pondence in the non-Hermitian case.\n\n[1] L. Lu\, J. D. Joannopoulos\, M. Soljačić\, "Topological photonics"\, Nat. Photonics\, 8\, 821\, (2014). \n\n[2] M. G. Silveirinha\, "Topological theory of non-Hermitian photonic systems"\, Phys. Rev. B\, 99\, 125155\, 2019.\n\n[3] F. R. Prudêncio\, M. G. Silveirinha\, First Principles Calculation of Topological Invariants o f non-Hermitian Photonic Crystals\, arXiv:2003.01539\n LOCATION:https://stable.researchseminars.org/talk/QM3/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Manuel Asorey (University of Zaragoza) DTSTART:20200708T100000Z DTEND:20200708T110000Z DTSTAMP:20260404T094545Z UID:QM3/8 DESCRIPTION:Title: Bulk-Edge dualities in Topological Matter\nby Manuel Asorey (Univer sity of Zaragoza) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n \nAbstract\nNovel bulk-edge dualities have recently emerged in topological materials from the observation of some phenomenological correspondences. The similarity of these dualities with string theory dualities is very app ealing and has boosted a quite significant number of cross field studies.\ nWe analyze the bulk-edge dualities in the integer quantum Hall effect\, w here due to the simpler nature of planar systems the duality can be analyz ed by powerful analytic techniques. The results show that the corresponden ce is less robust than expected. In particular\, it is highly dependent of the type of boundary conditions of the topological material. We introduce a formal proof of the equivalence of bulk and edge approaches to the quan tization of Hall conductivity for metallic plates with local boundary cond itions. However\, the proof does not work for non-local boundary condition s\, like the Atiyah-Patodi-Singer boundary conditions\, due to the appeara nce of gaps between the bulk and edge states.\n LOCATION:https://stable.researchseminars.org/talk/QM3/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Giandomenico Palumbo (Université Libre de Bruxelles) DTSTART:20200713T160000Z DTEND:20200713T170000Z DTSTAMP:20260404T094545Z UID:QM3/9 DESCRIPTION:Title: Four-dimensional semimetals with tensor monopoles: from surface states to topological responses\nby Giandomenico Palumbo (Université Libre d e Bruxelles) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbs tract\nQuantum anomalies offer a useful guide for the exploration of trans port phenomena in topological semimetals. A prominent example is provided by the chiral magnetic effect in three-dimensional Weyl semimetals\, which stems from the chiral anomaly. Here\, we reveal a distinct quantum effect \, coined "parity magnetic effect"\, which is induced by the parity anomal y in a four-dimensional topological semimetal. Upon preserving time-revers al symmetry\, the spectrum of our model is doubly degenerate and the nodal (Dirac) points behave like Z2 monopoles. When time-reversal symmetry is b roken\, while preserving the sublattice (chiral) symmetry\, our system sup ports spin- 3/2 quasiparticles and the corresponding Dirac-like cones host tensor monopoles characterized by a Z number\, the Dixmier-Douady invaria nt. In both cases\, the semimetal exhibits topologically protected Fermi a rcs on its boundary. Besides its theoretical implications in both condense d matter and quantum field theory\, the peculiar 4D magnetic effect reveal ed by our model could be measured by simulating higher-dimensional semimet als in synthetic matter.\n LOCATION:https://stable.researchseminars.org/talk/QM3/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Raffaele Resta (Instituto Officina dei Materiali\, CNR\, Trieste\, Italy) DTSTART:20200629T160000Z DTEND:20200629T170000Z DTSTAMP:20260404T094545Z UID:QM3/10 DESCRIPTION:Title: The insulating state of matter: a geometrical theory\nby Raffaele Resta (Instituto Officina dei Materiali\, CNR\, Trieste\, Italy) as part o f Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nThe insulating versus conducting behavior of condensed matter is commonly addressed\nin t erms of electronic excitations and/or conductivity. At variance with such wisdom\, W. Kohn hinted in 1964 that the insulating state of matter reflec ts a peculiar organization of the electrons in their ground state\, and do es not require an energy gap.\nKohn’s “theory of the insulating state ” got a fresh restart in 1999\; at the root of these\ndevelopments is th e modern theory of polarization\, developed in the early 1990s\, and\nbase d on a geometrical concept (Berry phase). Since insulators and metals pola rize\nin a qualitatively different way\, quantum geometry also discriminat es insulators\nfrom conductors. A common geometrical “marker”\, based on the quantum metric\,\ncaracterizes all insulators (band insulators\, An derson insulators\, Mott insulators\,\nquantum Hall insulators. . . )\; su ch marker diverges in conductors.\n LOCATION:https://stable.researchseminars.org/talk/QM3/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Lucas Sá (Instituto Superior Técnico and CEFEMA) DTSTART:20200617T100000Z DTEND:20200617T110000Z DTSTAMP:20260404T094545Z UID:QM3/11 DESCRIPTION:Title: Random matrix theory of dissipative quantum chaos\nby Lucas Sá (I nstituto Superior Técnico and CEFEMA) as part of Quantum Matter meets Mat hs (IST\, Lisbon)\n\n\nAbstract\nDescribing complex interacting quantum sy stems is a daunting task. One very fruitful approach to this problem\, dev eloped for unitary dynamics\, is to represent the Hamiltonian of a system by a large random matrix. This eventually led to the development of the fi eld of quantum chaos. Arguably\, one of its most spectacular achievements was the identification of universal signatures of chaos in quantum systems \, characterizing the correlations of their energy levels. In this talk\, we will focus on the recent application of (non-Hermitian) random matrix t heory to open quantum systems\, where dissipation and decoherence coexist with unitary dynamics. First\, we will discuss a class of stochastic Lindb ladians with random Hamiltonian and independent random dissipation channel s (jump operators)\, as a model for the generator of complicated nonunitar y dynamics. We will then explain what difficulties arise when combining di ssipation with quantum chaos\, and how to overcome them. In particular\, w e discuss a new non-Hermitian random matrix ensemble with eigenvalues on t he torus and how it connects to our recent proposal of using complex spaci ng ratios as a signature of dissipative quantum chaos.\n LOCATION:https://stable.researchseminars.org/talk/QM3/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Christophe Garban (Université Lyon 1) DTSTART:20200720T160000Z DTEND:20200720T170000Z DTSTAMP:20260404T094545Z UID:QM3/12 DESCRIPTION:Title: A new point of view on topological phase transitions\nby Christoph e Garban (Université Lyon 1) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nTopological phase transitions were discovered by B erezinskii-Kosterlitz-Thouless in the 70's. They describe intriguing phase transitions for classical spins systems such as the plane rotator model ( or $XY$ model). I will start by reviewing how this phase transition arises in cases such as:\n\nthe $XY$ model (spins on $\\mathbb{Z}^2$ with values in the unit circle)\nthe integer-valued Gaussian Free Field (or $\\mathbb {Z}$-ferromagnet)\nAbelian Yang-Mills on $\\mathbb{Z}^4$\nI will then conn ect topological phase transitions to a statistical reconstruction problem concerning the Gaussian Free Field and will show that the feasibility of t he reconstruction undergoes a KT transition.\n\nThis is a joint work with Avelio Sepúlveda (Lyon) and the talk will be based mostly on the preprint : https://arxiv.org/abs/2002.12284\n LOCATION:https://stable.researchseminars.org/talk/QM3/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Raquel Queiroz (Weizmann Institute of Science) DTSTART:20200727T160000Z DTEND:20200727T170000Z DTSTAMP:20260404T094545Z UID:QM3/13 DESCRIPTION:Title: Boundary Obstructed Topological Phases\nby Raquel Queiroz (Weizman n Institute of Science) as part of Quantum Matter meets Maths (IST\, Lisbo n)\n\n\nAbstract\nSymmetry protected topological (SPT) phases are gapped p hases of matter that cannot be deformed to a trivial phase without breakin g the symmetry or closing the bulk gap. Here\, we introduce a new notion o f a topological obstruction that is not captured by bulk energy gap closin gs in periodic boundary conditions. More specifically\, given a symmetric boundary termination we say two bulk Hamiltonians belong to distinct bound ­ary obstructed topological phases (BOTPs) if they can be deformed to eac h other on a system with periodic boundaries\, but cannot be deformed to e ach other in the open system without closing the gap at at least one high symmetry surface. BOTPs are not topological phases of matter in the standa rd sense since they are adiabat­ically deformable to each other on a toru s but\, similar to SPTs\, they are associated with boundary signatures in open systems such as surface states or fractional corner charges. In contr ast to SPTs\, these boundary signatures are not anomalous and can be remov ed by symmetrically adding lower dimensional SPTs on the boundary\, but th ey are stable as long as the spectral gap at high-symmetry edges/surfaces remains open. We show that the double-mirror quadrupole model of [Science\ , 357(6346)\, 2018] is a prototypical example of such phases\, and present a detailed analysis of several aspects of boundary obstructions in this m odel. In addition\, we intro­duce several three-dimensional models having boundary obstructions\, which are characterized either by surface states or fractional corner charges. We also provide a general framework to study boundary obstructions in free-fermion systems in terms of Wannier band re presentations (WBR)\, an extension of the recently-developed band represen tation formalism to Wannier bands. WBRs capture the notion of topological obstructions in the Wannier bands which can then be used to study topologi cal obstructions in the boundary spectrum by means of the correspondence b etween the Wannier and boundary spectra. This establishes a form of bulk-b oundary correspondence for BOTPs by relating the bulk band representation to the boundary topology.\n LOCATION:https://stable.researchseminars.org/talk/QM3/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Vincenzo Alba (University of Amsterdam) DTSTART:20200914T160000Z DTEND:20200914T170000Z DTSTAMP:20260404T094545Z UID:QM3/14 DESCRIPTION:Title: Hydrodynamic framework for out-of-equilibrium entangled many-body syst ems\nby Vincenzo Alba (University of Amsterdam) as part of Quantum Mat ter meets Maths (IST\, Lisbon)\n\n\nAbstract\nEntanglement and entropy are key concepts standing at the foundations of quantum and statistical mecha nics\, respectively. In the last decade the study of quantum quenches reve aled that these two concepts are intricately intertwined. For integrable m odels\, novel hydrodynamic approaches based on a quasiparticle picture eme rged as a new platform allowing for a quantitative understanding of quantu m information dynamics in quantum many-body systems. Remarkably\, this giv es fresh insights on how thermodynamics emerges in isolated out-of-equilib rium quantum systems.\n\nI will start by reviewing this new unifying frame work. I will then discuss several applications to entanglement-related qua ntities\, such as entanglement entropies\, mutual information\, logarithmi c negativity. I will also show how the framework allows to study the inter play between quantum information dynamics and transport of local conserved quantities. Finally\, I will derive some simple bounds on the quantum inf ormation scrambling in out-of-equilibrium systems.\n LOCATION:https://stable.researchseminars.org/talk/QM3/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Svetlana Jitomirskaya (University of California\, Irvine) DTSTART:20200907T160000Z DTEND:20200907T170000Z DTSTAMP:20260404T094545Z UID:QM3/15 DESCRIPTION:Title: Anderson localization and local eigenvalue statistics\nby Svetlana Jitomirskaya (University of California\, Irvine) as part of Quantum Matte r meets Maths (IST\, Lisbon)\n\n\nAbstract\nPoisson local statistics of e igenvalues is widely accepted as a necessary signature of Anderson localiz ation\, but so far has been rigorously established only for random systems . We will argue that this paradigm is wrong\, and the reality is a lot mor e complex and interesting\, by presenting both rigorous results for the Ha rper and Maryland models and numerics for other quasiperiodic and similar models with localization. We will also discuss a conjecture on what the di stribution is in the general ergodic situation.\n LOCATION:https://stable.researchseminars.org/talk/QM3/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Masud Haque (Maynooth University) DTSTART:20201012T160000Z DTEND:20201012T170000Z DTSTAMP:20260404T094545Z UID:QM3/16 DESCRIPTION:Title: Eigenstate Thermalization\, random matrices and (non)local operators i n many-body systems\nby Masud Haque (Maynooth University) as part of Q uantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nThe eigenstate the rmalization hypothesis (ETH) is a cornerstone in our understanding of quan tum statistical mechanics. The extent to which ETH holds for nonlocal oper ators (observables) is an open question. I will address this question usin g an analogy with random matrix theory. The starting point will be the con struction of extremely non-local operators\, which we call Behemoth operat ors. The Behemoths turn out to be building blocks for all physical operato rs. This construction allow us to derive scalings for both local operators and different kinds of nonlocal operators.\n LOCATION:https://stable.researchseminars.org/talk/QM3/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Gil Refael (Institute for Quantum Information and Matter) DTSTART:20200921T160000Z DTEND:20200921T170000Z DTSTAMP:20260404T094545Z UID:QM3/17 DESCRIPTION:Title: Floquet higher-order topological insulators: principles and path towar ds realizations\nby Gil Refael (Institute for Quantum Information and Matter) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract \nThe co-existence of spatial and non-spatial symmetries together with app ropriate commutation/anticommutation relations between them can give rise to static higher-order topological phases\, which host gapless boundary mo des of co-dimension higher than one. Alternatively\, space-time symmetries in a Floquet system can also lead to anomalous Floquet boundary modes of higher co-dimensions\, with different commutation/anticommutation relation s with respect to non-spatial symmetries. In my talk I will review how the se dynamical analogs of the static HOTI's emerge\, and also show how a coh erently excited phonon mode can be used to support non-trivial Floquet hig her-order topological phases. If time allows\, I will also review recent w ork on Floquet engineering and band flattening of twisted-bilayer graphene .\n LOCATION:https://stable.researchseminars.org/talk/QM3/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Tom Claeys (Université Catholique de Louvain) DTSTART:20200928T160000Z DTEND:20200928T170000Z DTSTAMP:20260404T094545Z UID:QM3/18 DESCRIPTION:Title: Deformed Airy kernel determinants: from KPZ tails to initial data for KdV\nby Tom Claeys (Université Catholique de Louvain) as part of Quan tum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nFredholm determinants associated to deformations of the Airy kernel are closely connected to th e solution to the Kardar-Parisi-Zhang (KPZ) equation with narrow wedge ini tial data\, and they also appear as largest particle distribution in model s of positive-temperature free fermions. I will explain how logarithmic de rivatives of the Fredholm determinants can be expressed in terms of a $2\\ times 2$ Riemann-Hilbert problem.\nThis Riemann-Hilbert representation can be used to derive precise lower tail asymptotics for the solution of the KPZ equation with narrow wedge initial data\, refining recent results by C orwin and Ghosal\, and it reveals a remarkable connection with a family of unbounded solutions to the Korteweg-de Vries (KdV) equation and with an i ntegro-differential version of the Painlevé II equation.\n LOCATION:https://stable.researchseminars.org/talk/QM3/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Barry Simon (Caltech) DTSTART:20201019T120000Z DTEND:20201019T130000Z DTSTAMP:20260404T094545Z UID:QM3/19 DESCRIPTION:Title: Berry's Phase\, TKN$^2$ Integers and All That: My work on Topology in Condensed Matter\nby Barry Simon (Caltech) as part of Quantum Matter m eets Maths (IST\, Lisbon)\n\n\nAbstract\nI will give an overview of my wor k on topological methods in condensed matter physics almost 40 years ago. Include will be Homotopy and TKN$^2$ integers\, holonomy and Berry's phase and quarternions and Berry's phase for Fermions. If time allows\, I'll di scuss supersymmetry and pairs of projections.\n LOCATION:https://stable.researchseminars.org/talk/QM3/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Joseph Maciejko (University of Alberta) DTSTART:20201026T170000Z DTEND:20201026T180000Z DTSTAMP:20260404T094545Z UID:QM3/20 DESCRIPTION:Title: Hyperbolic band theory\nby Joseph Maciejko (University of Alberta) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nThe n otions of Bloch wave\, crystal momentum\, and energy bands are commonly re garded as unique features of crystalline materials with commutative transl ation symmetries. Motivated by the recent realization of hyperbolic lattic es in circuit QED\, I will present a hyperbolic generalization of Bloch th eory\, based on ideas from Riemann surface theory and algebraic geometry. The theory is formulated despite the non-Euclidean nature of the problem a nd concomitant absence of commutative translation symmetries. The general theory will be illustrated by examples of explicit computations of hyperbo lic Bloch wavefunctions and bandstructures.\n LOCATION:https://stable.researchseminars.org/talk/QM3/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Benoît Douçot (LPTHE\, CNRS and Sorbonne Université\, Paris) DTSTART:20201109T160000Z DTEND:20201109T170000Z DTSTAMP:20260404T094545Z UID:QM3/21 DESCRIPTION:Title: Spin textures in quantum Hall ferromagnets\nby Benoît Douçot (LP THE\, CNRS and Sorbonne Université\, Paris) as part of Quantum Matter mee ts Maths (IST\, Lisbon)\n\n\nAbstract\nIn the presence of a strong magneti c field\, and for an integer filling of the Landau levels\, Coulomb intera ctions favor a ferromagnetic ground-state. It has been shown already twent y years ago\, both theoretically and experimentally\, that when extra char ges are added or removed to such systems\, the ferromagnetic state becomes unstable and is replaced by spin textures called Skyrmions. We have gener alized this notion to an arbitrary number $N$ of internal states for the e lectrons\, which may correspond to the combination of spin\, valley\, or l ayer indices. The first step is to associate a many electron wave-function \, projected on the lowest Landau level\, to any classical spin texture de scribed by a smooth map from the plane to the projective space $\\mathbb{C P}^{N-1}$. In the large magnetic field limit\, we assume that the spin tex ture is slowly varying on the scale of the magnetic length\, which allows us to evaluate the expectation value of the interaction Hamiltonian on the se many electron quantum states. The first non trivial term in this semi-c lassical expansion is the usual $\\mathbb{CP}^{N-1}$ non-linear sigma mode l\, which is known to exhibit a remarkable degeneracy of the many electron states obtained from holomorphic textures. Surprisingly\, this degeneracy is not lifted by reintroducing quantum fluctuations. It is eventually lif ted by the sub-leading term in the effective Hamiltonian\, which selects a hexagonal Skyrmion lattice and therefore breaks both translational and in ternal $SU(N)$ symmetries. I will show that these optimal classical textur es can be interpreted in an appealing way using geometric quantization.\n LOCATION:https://stable.researchseminars.org/talk/QM3/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Jiannis K. Pachos (University of Leeds) DTSTART:20201116T170000Z DTEND:20201116T180000Z DTSTAMP:20260404T094545Z UID:QM3/22 DESCRIPTION:Title: Less is more: effective description of topological spin liquids\nb y Jiannis K. Pachos (University of Leeds) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nIt is widely accepted that topological superconductors can only have an effective interpretation in terms of cur ved geometry rather than gauge fields due to their charge neutrality. This approach is commonly employed in order to investigate their properties\, such as the behaviour of their energy currents\, though we do not know how accurate it is. I will show that the low-energy properties of the Kitaev honeycomb lattice model\, such as the shape of Majorana zero modes or the deformations of the correlation length\, are faithfully described in terms of Riemann-Cartan geometry. Moreover\, I will present how effective axial gauge fields can couple to Majorana fermions\, thus giving a unified pict ure between vortices and lattice dislocations that support Majorana zero m odes.\n LOCATION:https://stable.researchseminars.org/talk/QM3/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Gourab Ray (University of Victoria) DTSTART:20201130T170000Z DTEND:20201130T180000Z DTSTAMP:20260404T094545Z UID:QM3/23 DESCRIPTION:Title: Universality of dimers via imaginary geometry\nby Gourab Ray (Univ ersity of Victoria) as part of Quantum Matter meets Maths (IST\, Lisbon)\n \n\nAbstract\nThe dimer model is a model of uniform perfect matching and i s one of the fundamental models of statistical physics. It has many deep a nd intricate connections with various other models in this fiel\, namely t he Ising model and the six-vertex model.\n\nThis model has received a lot of attention in the mathematics community in the past two decades. The pri mary reason behind such popularity is that this model is integrable\, in p articular\, the correlation functions can be represented exactly in a dete rminental form. This gives rise to a rich interplay between algebra\, geom etry\, probability and theoretical physics.\nFor graphs with very regular local structures\, exact computations of the correlation functions are pos sible by Kasteleyn theory. R. Kenyon pioneered the development of the subj ect in this direction by proving that the fluctuations of the height funct ion associated to the dimer model on the square lattice converges to the G aussian free field (a conformally invariant Gaussian field). However\, suc h computations seem only possible on graphs with special local structures\ , while the dimer model is supposed to have GFF type fluctuations in a muc h more general setting.\n\nIn this talk\, I will give an overview of an on going project with N\, Berestycki (U. Vienna) and B. Laslier (Paris—Dide rot 7) where we establish a form of universality about the GFF fluctuation of the dimer model. Our approach does not use Kasteleyn theory\, but uses a mapping known since Temperley—Fisher\, which maps the dimer model to uniform spanning trees. Remarkably\, as observed by Benjamini\, the “win ding” of the branches of this spanning tree exactly measures the height function of the dimers. We combine this approach with the developing unive rsal scaling limit results of the uniform spanning trees\, revolutionized by Schramm through the discovery of SLE. We show that the continuum ``wind ing” of these continuum limiting spanning trees converge to the GFF and harness from this the universality of the scaling limit. A key input in id entifying the limit is the so-called imaginary geometry developed by Mille r and Sheffield. In a more recent work\, we extend this universality parti ally to general Riemann surfaces as well.\n\nThis talk is based on the fol lowing preprints and some works in progress.\n\nhttps://projecteuclid.org/ euclid.aop/1585123322
\nhttps://arxiv.org/abs/1610.07994
\nhttps:/ /arxiv.org/abs/1908.00832\n LOCATION:https://stable.researchseminars.org/talk/QM3/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Enej Ilievski (University of Ljubljana) DTSTART:20201102T170000Z DTEND:20201102T180000Z DTSTAMP:20260404T094545Z UID:QM3/24 DESCRIPTION:Title: Superuniversality of superdiffusion\nby Enej Ilievski (University of Ljubljana) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAb stract\nEmergence of anomalous transport laws in deterministic interacting many-body systems has become a subject of intense study in the past few y ears. One of the most prominent examples is the unexpected discovery of su perdiffusive spin dynamics in the isotropic Heisenberg quantum spin chain with at half filling\, which falls into the universality class of the cele brated Kardar-Parisi-Zhang equation. In this talk\, we will theoretically justify why the observed superdiffusion of the Noether charges with anomal ous dynamical exponent $z=3/2$ is indeed superuniversal\, namely it is a f eature of all integrable interacting lattice models or quantum field theor ies which exhibit globally symmetry of simple Lie group $G$\, in thermal e nsembles that do not break $G$-invariance. The phenomenon can be attribute d to thermally dressed giant quasiparticles\, whose properties can be trac ed back to fusion relations amongst characters of quantum groups called Ya ngians. Giant quasiparticles can be identified with classical solitons\, i .e. stable nonlinear solutions to certain integrable PDE representing clas sical ferromagnet field theories on certain types of coset manifolds. We s hall explain why these inherently semi-classical objects are in one-to-one correspondence with the spectrum of Goldstone modes. If time permits\, we shall introduce another type of anomalous transport law called undular di ffusion that generally occurs amongst the symmetry-broken Noether fields i n $G$-invariant dynamical systems at finite charge densities.\n LOCATION:https://stable.researchseminars.org/talk/QM3/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Eslam Khalaf (Harvard University) DTSTART:20201123T170000Z DTEND:20201123T180000Z DTSTAMP:20260404T094545Z UID:QM3/25 DESCRIPTION:Title: Localization at the edge of a topological insulator: Interplay of diso rder-induced-localization and topological protection\nby Eslam Khalaf (Harvard University) as part of Quantum Matter meets Maths (IST\, Lisbon)\ n\n\nAbstract\nTransport in disordered one-dimensional wires is described by diffusion at short distances/times and by Anderson localization at long distances/times. I will investigate how this picture is altered in a diso rdered multi-channel wire where some of the channels are topologically pro tected. This scenario can be realized at the interface between two quantum Hall systems\, in a Weyl semimetal in a magnetic field or at the edge of a quantum spin Hall insulator. Technically\, the problem is described by a $0+1$-dimensional field theory in the form of a supersymmetric non-linear sigma model with a topological term. I will show how to solve this field theory exactly to obtain DC (static) transport quantities such as DC condu ctance and shot noise as well as dynamical responses such as diffusion pro bability of return and correlations of local density of states. I will dis cuss several surprising findings of this exact solution. First\, I find th at disorder is much more effective in localizing the diffusive channels in the presence of topologically protected ones. This can be understood in t erms of statistical level repulsion by mapping the problem to that of a ra ndom matrix ensemble with zero eigenvalues. Second\, I find that localizat ion corrections dramatically alter the long time behavior of the return pr obability in a system described by diffusion+drift equation at the classic al level. Finally\, I find that in a disordered wire with topologically pr otected channels\, the wave functions display level attraction rather than level repulsion.\n LOCATION:https://stable.researchseminars.org/talk/QM3/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Lev Vidmar (Jozef Stefan Institute and University of Ljubljana) DTSTART:20201207T170000Z DTEND:20201207T180000Z DTSTAMP:20260404T094545Z UID:QM3/26 DESCRIPTION:Title: Entanglement entropy in many-body eigenstates of local Hamiltonians\nby Lev Vidmar (Jozef Stefan Institute and University of Ljubljana) as p art of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nThe eigens tate entanglement entropy is a powerful tool to distinguish integrable fro m generic quantum-chaotic Hamiltonians. In integrable models\, the average eigenstate entanglement entropy (over all Hamiltonian eigenstates) has a volume-law coefficient that generally depends on the subsystem fraction. I n contrast\, the volume-law coefficient is maximal (subsystem fraction ind ependent) in quantum-chaotic models. In the seminar I will present an over view of our current understanding of bipartite entanglement entropies in m any-body quantum states above the ground states\, and contrast analytical predictions with numerical results for eigenstates of physical Hamiltonian s.\n LOCATION:https://stable.researchseminars.org/talk/QM3/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Takashi Oka (University of Tokyo) DTSTART:20201214T100000Z DTEND:20201214T110000Z DTSTAMP:20260404T094545Z UID:QM3/27 DESCRIPTION:Title: Floquet Engineering of Quantum Materials\nby Takashi Oka (Universi ty of Tokyo) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbs tract\n

Periodic driving of quantum systems is attracting interest since we can use it to realize new states of matter with exotic properties. Thi s concept\, known as Floquet engineering\, has been widely used in cold at oms [1] and recently in solid-state systems [2]. In this talk\, I plan to explain Floquet engineering basics using simple examples such a 2D and 3D Dirac electrons in circularly polarized laser fields [2]. Then\, to develo p a more in-depth and intuitive understanding of Floquet states\, I will e xplain an example of a dynamical Landau quantization realized in oscillati ng magnetic fields.

\n\n\n

[1] A. Eckardt\, Rev. Mod. Phys. 89\, 0 11004 (2017).
\n[2] T. Oka\, S. Kitamura\, Annual Reviews of CMP\, 10:387 (2019).
\n[3] T. Oka\, L. Bucciantini\, Phys . Rev. B 94\, 155133 (2016).

\n LOCATION:https://stable.researchseminars.org/talk/QM3/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Berry (University of Bristol) DTSTART:20210111T170000Z DTEND:20210111T180000Z DTSTAMP:20260404T094545Z UID:QM3/28 DESCRIPTION:Title: Geometric phases and the separation of the world\nby Michael Berry (University of Bristol) as part of Quantum Matter meets Maths (IST\, Lisb on)\n\n\nAbstract\nThe waves that describe systems in quantum physics can carry information about how their environment has been altered\, for examp le by forces acting on them. This effect is the geometric phase. It also o ccurs in the optics of polarised light\, where it goes back to the 1830s\; and it gives insight into the spin-statistics relation for identical quan tum particles. The underlying mathematics is geometric: the phenomenon of parallel transport\, which also explains how falling cats land on their fe et\, and why parking a car in a narrow space is difficult. Incorporating t he back-reaction of the geometric phase on the dynamics of the changing en vironment exposes the unsolved problem of how strictly a system can be sep arated from a slowly-varying environment\, and involves different mathemat ics: divergent infinite series.\n LOCATION:https://stable.researchseminars.org/talk/QM3/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Sthitadhi Roy (University of Oxford) DTSTART:20210118T170000Z DTEND:20210118T180000Z DTSTAMP:20260404T094545Z UID:QM3/29 DESCRIPTION:Title: Many-body localisation: a tale of correlations and classical percolati on on Fock space\nby Sthitadhi Roy (University of Oxford) as part of Q uantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nMany-body localise d (MBL) phases of matter fall outside the conventional paradigm of equilib rium statistical mechanics and thermodynamics. A natural question thus is\ , what minimal and generic properties must random many-body Hamiltonians p ossess for a localised phase to be stable? In this talk\, I will address t he question by exploiting the exact mapping between a many-body Hamiltonia n and a tight-binding problem on the Fock-space graph. In particular\, I w ill present a theory for how the strong correlations in the effective Fock -space disorder play a central role in stabilising an MBL phase. The theo ry is rooted in analytic but approximate calculations of the propagators o n the Fock space. To shed further light on the underlying physics\, I will also introduce and discuss a classical proxy for the MBL transition in th e form of a percolation transition on the Fock space. Finally\, I will dis cuss a novel class of Anderson localisation problems on correlated trees\, to understand the effect of such disorder correlations in a more controll ed setting.\n LOCATION:https://stable.researchseminars.org/talk/QM3/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Subir Sachdev (Harvard University) DTSTART:20210104T170000Z DTEND:20210104T180000Z DTSTAMP:20260404T094545Z UID:QM3/30 DESCRIPTION:Title: A simple model of entangled qubits: how it describes superconductors a nd black holes\nby Subir Sachdev (Harvard University) as part of Quant um Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nLong-range\, multi-par ticle quantum entanglement plays a fundamental role in our understanding o f many modern quantum materials\, including the copper-based high temperat ure superconductors. Hawking's quantum information puzzle in the quantum t heory of black holes also involves non-local entanglement. I will describe a simple model of randomly entangled qubits which has shed light on these distinct fields of physics.\n LOCATION:https://stable.researchseminars.org/talk/QM3/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Steve Simon (University of Oxford) DTSTART:20210125T170000Z DTEND:20210125T180000Z DTSTAMP:20260404T094545Z UID:QM3/31 DESCRIPTION:Title: Lattice Geometry Dependence and Independence: Important Applications of a Simple Law\nby Steve Simon (University of Oxford) as part of Quan tum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nThe ability to create and manipulate optical lattices for cold atoms\, with a view towards stud ying topological matter\, has brought renewed focus to the physics of Bloc h waves and the role of the lattice in governing their properties. We cons ider generic tight binding models where particle motion is described in te rms of hopping amplitudes between orbitals. The physical attributes of the orbitals\, including their locations in space\, are independent pieces of information. We identify a notion of geometry-independence: any physical quantity that depends only on the tight-binding parameters (and not on the explicit information about the orbital geometry) is said to be "geometry- independent." Identification of geometry-dependent vs. independent quantit ies can be used as a novel principle for constraining a variety of results in both non-interacting and interacting systems. We show\, e.g.\, how Hal l measurements based on accelerated lattices or tilted potentials\, and th ose based on applying a chemical potential imbalance between reservoirs\, give different results due to the fact that one is geometry-dependent\, wh ile the other is geometry-independent. Similar considerations apply for th ermal Hall responses in electronic\, cold atomic\, and spin systems.\n\n\n Ref:\n\nSteven H. Simon and Mark S. Rudner\, Phys. Rev. B 102\, 165148\, 2 020.\n LOCATION:https://stable.researchseminars.org/talk/QM3/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Rémy Mosseri (LPTMC Sorbonne Université) DTSTART:20210208T100000Z DTEND:20210208T110000Z DTSTAMP:20260404T094545Z UID:QM3/32 DESCRIPTION:Title: Liquid crystal director fields in three-dimensional non-Euclidean geom etries\nby Rémy Mosseri (LPTMC Sorbonne Université) as part of Quant um Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nThis work investigates nematic liquid crystals in three-dimensional curved space\, and determine s which director deformation modes are compatible with each possible type of non-Euclidean geometry. Previous work by Sethna et al. [1] showed that double twist is frustrated in flat space $\\mathbb{R}^3$\, but can fit per fectly in the hypersphere $\\mathbb{S}^3$. Here\, we extend that work to a ll four deformation modes (splay\, twist\, bend\, and biaxial splay) and a ll eight Thurston geometries [2]. Each pure mode of director deformation c an fill space perfectly\, for at least one type of geometry. This analysis shows the ideal structure of each deformation mode in curved space\, whic h is frustrated by the requirements of flat space.\n\n[1] Sethna J P\,Wrig ht D C and Mermin N D 1983 Phys. Rev. Lett. 51 467–70\n\n[2] J-F Sadoc\, R. Mosseri and J. Selinger\, New Journal of Physics 22 (2020) 093036\n LOCATION:https://stable.researchseminars.org/talk/QM3/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Maciej Koch-Janusz (University of Zurich) DTSTART:20210222T170000Z DTEND:20210222T180000Z DTSTAMP:20260404T094545Z UID:QM3/33 DESCRIPTION:Title: Statistical physics through the lens of real-space mutual information< /a>\nby Maciej Koch-Janusz (University of Zurich) as part of Quantum Matte r meets Maths (IST\, Lisbon)\n\n\nAbstract\nIdentifying the relevant coars e-grained degrees of freedom in a complex physical system is a key stage i n developing effective theories. The renormalization group (RG) provides a framework for this task\, but its practical execution in unfamiliar syste ms is fraught with ad hoc choices. Machine learning approaches\, on the ot her hand\, though promising\, often lack formal interpretability: it is un clear what relation\, if any\, the architecture- and training-dependent le arned "relevant" features bear to standard objects of physical theory.\n\n I will present recent results addressing both issues. We develop a fast al gorithm\, the RSMI-NE\, employing state-of-art results in machine-learning -based estimation of information-theoretic quantities to construct the opt imal coarse-graining. We use it to develop a new approach to identifying t he most relevant field theory operators describing a statistical system\, which we validate on the example of interacting dimer model. I will also d iscuss formal results underlying the method: we establish equivalence betw een the information-theoretic notion of relevance defined in the Informati on Bottleneck (IB) formalism of compression theory\, and the field-theoret ic relevance of the RG. We show analytically that for statistical physical systems the "relevant" degrees of freedom found using IB compression inde ed correspond to operators with the lowest scaling dimensions\, providing a dictionary connecting two distinct theoretical toolboxes.\n LOCATION:https://stable.researchseminars.org/talk/QM3/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Markus Heyl (Max-Planck Institute for the Physics of Complex Syste ms\, Dresden) DTSTART:20210322T170000Z DTEND:20210322T180000Z DTSTAMP:20260404T094545Z UID:QM3/34 DESCRIPTION:Title: Quantum many-body dynamics in two dimensions with artificial neural ne tworks\nby Markus Heyl (Max-Planck Institute for the Physics of Comple x Systems\, Dresden) as part of Quantum Matter meets Maths (IST\, Lisbon)\ n\n\nAbstract\nIn the last two decades the field of nonequilibrium quantum many-body physics has seen a rapid development driven\, in particular\, b y the remarkable progress in quantum simulators\, which today provide acce ss to dynamics in quantum matter with an unprecedented control. However\, the efficient numerical simulation of nonequilibrium real-time evolution i n isolated quantum matter still remains a key challenge for current comput ational methods especially beyond one spatial dimension. In this talk I wi ll present a versatile and efficient machine learning inspired approach. I will first introduce the general idea of encoding quantum many-body wave functions into artificial neural networks. I will then identify and resolv e key challenges for the simulation of real-time evolution\, which previou sly imposed significant limitations on the accurate description of large s ystems and long-time dynamics. As a concrete example\, I will consider the dynamics of the paradigmatic two-dimensional transverse field Ising model \, where we observe collapse and revival oscillations of ferromagnetic ord er and demonstrate that the reached time scales are comparable to or excee d the capabilities of state-of-the-art tensor network methods.\n LOCATION:https://stable.researchseminars.org/talk/QM3/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Anatoli Polkovnikov (Boston University) DTSTART:20210315T170000Z DTEND:20210315T180000Z DTSTAMP:20260404T094545Z UID:QM3/35 DESCRIPTION:Title: Eigenstate deformations as a sensitive probe of quantum chaos\nby Anatoli Polkovnikov (Boston University) as part of Quantum Matter meets Ma ths (IST\, Lisbon)\n\n\nAbstract\nIn this talk I will discuss how one can detect quantum chaos in generic interacting models using adiabatic transfo rmations\, specifically the fidelity susceptibility. In particular\, I wil l show that it exhibits a very sharp crossover behavior from the algebraic to the exponential scaling form with the system size in the presence of a small integrability breaking parameter. This sensitivity allows one to id entify tiny integrability breaking perturbations\, not detectable by conve ntional methods. I will also discuss that generically integrable and chaot ic regimes are separated by a universal regime of “maximal chaos” wher e the fidelity susceptibility saturates its upper bound and the system exh ibits exponentially slow\, glassy dynamics. I will illustrate how this pro be works using several examples of both clean and disordered systems and\, in particular\, will argue that numerical results indicate absence of a c ontinuous many-body localization transition in the thermodynamic limit.\n LOCATION:https://stable.researchseminars.org/talk/QM3/35/ END:VEVENT BEGIN:VEVENT SUMMARY:David J. Luitz (Max Planck Institute for the Physics of Complex Sy stems\, Dresden) DTSTART:20210412T160000Z DTEND:20210412T170000Z DTSTAMP:20260404T094545Z UID:QM3/36 DESCRIPTION:Title: Hierarchy of Relaxation Timescales in Local Random Liouvillians\nb y David J. Luitz (Max Planck Institute for the Physics of Complex Systems\ , Dresden) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstr act\nTo characterize the generic behavior of open quantum many-body system s\, we consider random\, purely dissipative Liouvillians with a notion of locality. We find that the positivity of the map implies a sharp separatio n of the relaxation timescales according to the locality of observables. S pecifically\, we analyze a spin-$1/2$ system of size $\\ell$ with up to n -body Lindblad operators\, which are n local in the complexity-theory sens e. Without locality ($n=l$)\, the complex Liouvillian spectrum densely cov ers a “lemon”-shaped support\, in agreement with recent findings [S. D enisov et al.\, Phys. Rev. Lett. 123\, 140403 (2019)\, L. Sa et al.\, JPA 53\, 305303].\nHowever\, for local Liouvillians ($n < l$)\, we find that t he spectrum is composed of several dense clusters with random matrix spaci ng statistics\, each featuring a lemon-shaped support wherein all eigenvec tors correspond to $n$-body decay modes. This implies a hierarchy of relax ation timescales of n-body observables\, which we verify to be robust in t he thermodynamic limit. Our findings for n locality generalize immediately to the case of spatial locality\, introducing further splitting of timesc ales due to the additional structure. \n\nTo test our theoretical predict ion\, we perform experiments on the IBM quantum computing platform\, desig ning different "waiting circuits" to inject two body dissipative interacti ons by two qubit entangling gates. We find excellent agreement with our th eory and observe the predicted hierarchy of timescales.\n\n\n\n\n\n[1] K. Wang\, F. Piazza\, D. J. Luitz ” Hierarchy of relaxation timescales in l ocal random Liouvillians “ Phys. Rev. Lett. 124\, 100604 (2020)\n\n[2] O . E. Sommer\, F. Piazza\, and D. J. Luitz “Many-body Hierarchy of Dissip ative Timescales in a Quantum Computer” arXiv:2011.08853\n LOCATION:https://stable.researchseminars.org/talk/QM3/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Xiao-Gang Wen (Massachusetts Institute of Technology) DTSTART:20210426T160000Z DTEND:20210426T170000Z DTSTAMP:20260404T094545Z UID:QM3/37 DESCRIPTION:Title: A holographic view of symmetry -- symmetry as shadow of topological or der\nby Xiao-Gang Wen (Massachusetts Institute of Technology) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nRecently\, the notion of symmetry has been extended from 0-symmetry described by group t o higher symmetry described by higher group. In this talk\, we show that t he notion of symmetry can be generalized even further to "algebraic higher symmetry". Then we will describe an even more general point of view of sy mmetry\, which puts the (generalized) symmetry charges and topological exc itation at equal footing: symmetry can be viewed as gravitational anomaly\ , or symmetry can be viewed as shadow topological order in one higher dime nsion. This picture allows us to see many duality relations between seemin g unrelated symmetries.\n LOCATION:https://stable.researchseminars.org/talk/QM3/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Lea Santos (Yeshiva University) DTSTART:20210215T170000Z DTEND:20210215T180000Z DTSTAMP:20260404T094545Z UID:QM3/38 DESCRIPTION:Title: Indicators of quantum chaos and the transition from few- to many-body systems\nby Lea Santos (Yeshiva University) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nQuantum chaos\, especially when caused by particle interactions\, is closely related with topics of high e xperimental and theoretical interest\, from the thermalization of isolated systems to the difficulties to reach a localized phase\, and the emergenc e of quantum scars. In this talk\, various indicators of quantum chaos wil l be compared\, including level statistics\, structure of eigenstates\, ma trix elements of observables\, out-of-time ordered correlators\, and the c orrelation hole (ramp). These indicators are then employed to identify the minimum number of interacting particles required for the onset of strong chaos in quantum systems with short-range and also with long-range interac tions.\n\nRefs:\n\nhttps://arxiv.org/abs/2012.14436\nhttps://arxiv.org/abs /1802.08691\n LOCATION:https://stable.researchseminars.org/talk/QM3/38/ END:VEVENT BEGIN:VEVENT SUMMARY:David Tong (University of Cambridge) DTSTART:20210517T160000Z DTEND:20210517T170000Z DTSTAMP:20260404T094545Z UID:QM3/39 DESCRIPTION:Title: How to Give Chiral Fermions a Mass\nby David Tong (University of C ambridge) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstra ct\nChiral fermions have the property that their left-handed and right-han ded components transform differently under some symmetry. Folklore suggest s that it is impossible to give such fermions a mass without breaking this symmetry. I'll show\, through a number of examples\, why this folklore is wrong. In particular\, I'll show how one generation of fermions in the St andard Model can get a mass without the need for a Higgs boson that breaks electroweak symmetry.\n LOCATION:https://stable.researchseminars.org/talk/QM3/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Altland (University of Cologne) DTSTART:20210329T160000Z DTEND:20210329T170000Z DTSTAMP:20260404T094545Z UID:QM3/40 DESCRIPTION:Title: Spectral density of weakly disordered Weyl semimetals\nby Alexande r Altland (University of Cologne) as part of Quantum Matter meets Maths (I ST\, Lisbon)\n\n\nAbstract\nWeyl semimetals contain an even number of sing ular points in their Brillouin zone around which the dispersion is linear and the density of states (DoS) vanishes. How does the density of states c hange in the (inevitable) presence of impurities? This question has been t he subject of an intensive and partially controversial discussion in the r ecent literature. In particular\, it has been suggested that below a criti cal disorder strength the DoS remains zero\, and that the system supports a phase transition separating an intrinsically clean from a disordered pha se. In this talk\, I discuss this problem on the basis of several effectiv e models. All these support the integrity of the Weyl node and hence are c ompatible with the above scenario. I will also comment on the (tricky) com parison to numerics and point out a puzzle whose solution invites mathemat ical research.\n LOCATION:https://stable.researchseminars.org/talk/QM3/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Simon Becker (University of Cambridge) DTSTART:20210301T170000Z DTEND:20210301T180000Z DTSTAMP:20260404T094545Z UID:QM3/41 DESCRIPTION:Title: Mathematics of magic angles for twisted bilayer graphene\nby Simon Becker (University of Cambridge) as part of Quantum Matter meets Maths (I ST\, Lisbon)\n\n\nAbstract\nMagic angles are a hot topic in condensed matt er physics: when two sheets of graphene are twisted by those angles the re sulting material is superconducting. Please do not be scared by the physic s though: I will present a very simple operator whose spectral properties are thought to determine which angles are magical. It comes from a recent PR Letter by Tarnopolsky–Kruchkov–Vishwanath. The mathematics behind t his is an elementary blend of representation theory (of the Heisenberg gro up in characteristic three)\, Jacobi theta functions and spectral instabil ity of non-self-adjoint operators (involving Hoermander’s bracket condit ion in a very simple setting). The results will be illustrated by colourfu l numerics which suggest some open problems. This is joint work with M. Em bree\, J. Wittsten\, and M. Zworski.\n LOCATION:https://stable.researchseminars.org/talk/QM3/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Hannah Price (Birmingham University) DTSTART:20210308T170000Z DTEND:20210308T180000Z DTSTAMP:20260404T094545Z UID:QM3/42 DESCRIPTION:Title: Exploring 4D topological physics in the laboratory\nby Hannah Pric e (Birmingham University) as part of Quantum Matter meets Maths (IST\, Lis bon)\n\n\nAbstract\nSpatial dimensionality plays a key role in our underst anding of topological physics\, with different topological invariants need ed to characterise systems with different numbers of spatial dimensions. I n a 2D quantum Hall system\, for example\, a robust quantisation of the Ha ll response is related to the first Chern number: a 2D topological invaria nt of the electronic energy bands. Generalising to more spatial dimensions \, it was shown that a new type of quantum Hall effect could emerge in fou r dimensions\, but where the quantised response was related to a four-dime nsional topological invariant\, namely the second Chern number. While syst ems with four spatial dimensions may seem abstract\, recent developments i n ultracold atoms and photonics have opened the door to exploring such hig her-dimensional topological physics experimentally. In this talk\, I will introduce the theory of 4D topological phases of matter\, before discussin g recent experiments in cold atoms\, photonics and electrical circuits tha t have begun to probe aspects of this physics in the laboratory.\n LOCATION:https://stable.researchseminars.org/talk/QM3/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Karyn Le Hur (Centre de Physique Theorique\, École Polytechnique\ , CNRS) DTSTART:20210503T160000Z DTEND:20210503T170000Z DTSTAMP:20260404T094545Z UID:QM3/43 DESCRIPTION:Title: Geometry\, Light Response and Quantum Transport in Topological States of Matter\nby Karyn Le Hur (Centre de Physique Theorique\, École Poly technique\, CNRS) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n \nAbstract\nTopological states of matter are characterized by a gap in the bulk of the system referring to an insulator or a superconductor and topo logical edge modes as well which find various applications in transport an d spintronics. The bulk-edge correspondence is associated to a topological number. The table of topological states include the quantum Hall effect a nd the quantum anomalous Hall effect\, topological insulators and topologi cal superconductors in various dimensions and lattice geometries. Here\, w e discuss classes of states which can be understood from mapping onto a sp in-1/2 particle in the reciprocal space of wave-vectors. We develop a geom etrical approach on the associated Poincare-Bloch sphere\, developing smoo th fields\, which shows that the topology can be encoded from the poles on ly. We show applications for the light-matter coupling when coupling to ci rcular polarizations and develop a relation with quantum transport and the quantum Hall conductivity. The formalism allows to include interaction ef fects. We show our recent developments on a stochastic approach to englobe these interaction effects and discuss applications for the Mott transitio n of the Haldane and Kane-Mele models. Then\, we develop a model of couple d spheres and show the possibility of fractional topological numbers as a result of interactions between spheres and entanglement allowing a superpo sition of two geometries\, one encircling a topological charge and one rev ealing a Bell or EPR pair. Then\, we show applications of the fractional t opological numbers C=1/2 in bilayer honeycomb models describing topologica l semi-metals characterized by a quantized Berry phase at one Dirac point. \n\n- Joel Hutchinson and Karyn Le Hur\, arXiv:2002.11823 (under review)\n \n- Philipp Klein\, Adolfo Grushin\, Karyn Le Hur\, Phys. Rev. B 103\, 035 114 (2021)\n LOCATION:https://stable.researchseminars.org/talk/QM3/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Igor Lesanovsky (Universität Tübingen) DTSTART:20210524T160000Z DTEND:20210524T170000Z DTSTAMP:20260404T094545Z UID:QM3/44 DESCRIPTION:Title: Neural network dynamics in open quantum many-body systems\nby Igor Lesanovsky (Universität Tübingen) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nOpen quantum systems composed of atoms inte racting with light exhibit behaviour that is akin to that of associative m emories [1]. This means that they possess stationary states that can be\ni nterpreted as stored memory patterns\, which are retrieved when the initia l state is inside the basin of attraction of a given pattern [2]. The corr esponding pattern retrieval dynamics can be observed in actual experimenta l settings. In these experiments atoms are confined within an optical cavi ty whose photons mediate long-range interactions [3]. Stored patterns are encoded in the atom-light coupling constants. This setting offers an inter esting opportunity for studying quantum generalisations of associative mem ories and stored (quantum) patterns in this context [4]. Moreover\, it all ows to systematically construct scenarios in which quantum effects might b e beneficial\, e.g.\, for speeding up the pattern retrieval process [5]. I will talk about recent research of my group on this subject\, which build s a bridge between classic machine learning concepts\, such as the Hopfiel d Neural Network\, and most recent experimental manifestations of syntheti c quantum matter.\n\n\n\n[1] E. Fiorelli et al.\, Physical Review Letters 125\, 070604 (2020)\n\n[2] F. Carollo and I. Lesanovsky\, arXiv:2009.13932 (2020)\n\n[3] V.D. Vaidya et al.\, Physical Review X 8\, 011002 (2018)\n\ n[4] P. Rotondo et al.\, Journal of Physics A 51\, 115301 (2018)\n\n[5] E. Fiorelli et al.\, Physical Review A 99\, 032126 (2019)\n LOCATION:https://stable.researchseminars.org/talk/QM3/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Rubem Mondaini (Beijing Computational Science Research Center) DTSTART:20210628T160000Z DTEND:20210628T170000Z DTSTAMP:20260404T094545Z UID:QM3/45 DESCRIPTION:Title: Quantum Critical Points and the Sign Problem\nby Rubem Mondaini (B eijing Computational Science Research Center) as part of Quantum Matter me ets Maths (IST\, Lisbon)\n\n\nAbstract\nThe "sign problem" (SP) is the fun damental limitation to simulations of strongly correlated materials in con densed matter physics\, solving quantum chromodynamics at finite baryon de nsity\, and computational studies of nuclear matter. It is often argued th at the SP is not intrinsic to the physics of particular Hamiltonians\, sin ce the details of how it onsets\, and its eventual occurrence\, can be alt ered by the choice of algorithm or many-particle basis. Despite that\, I p lan to show in this talk that the SP in determinant quantum Monte Carlo (D QMC) is quantitatively linked to quantum critical behavior. This demonstra tion is done via simulations of a number of fundamental models of condense d matter physics\, all of whose critical properties are relatively well un derstood.\n LOCATION:https://stable.researchseminars.org/talk/QM3/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Gunter M. Schütz (Institute of Biological Information Processing and Institute for Advanced Simulation) DTSTART:20210419T160000Z DTEND:20210419T170000Z DTSTAMP:20260404T094545Z UID:QM3/46 DESCRIPTION:Title: Spin helix states in the dissipative Heisenberg quantum spin chain \nby Gunter M. Schütz (Institute of Biological Information Processing and Institute for Advanced Simulation) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nWe demonstrate that the exact nonequilibrium steady state of the one-dimensional Heisenberg $XXZ$ spin chain driven by boundary Lindblad operators can be constructed explicitly with a matrix p roduct ansatz for the nonequilibrium density matrix. For the isotropic Hei senberg chain\, polarized at the boundaries in different directions with a non-zero twist angle\, we calculate the exact magnetization profiles and magnetization currents. The in-plane steady-state magnetization profiles a re harmonic functions with a frequency proportional to the twist angle. In -plane steady-state magnetization currents are subdiffusive and vanish as the boundary coupling strength increases\, while the transverse current is diffusive and saturates as the coupling strength becomes large. The aniso tropic chain exhibits spin helix states at special values of the anisotrop y where the transverse current is independent of system size\, even for no n-integrable higher-spin chains.\n LOCATION:https://stable.researchseminars.org/talk/QM3/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Fleischhauer (Dept. of Physics & research center OPTIMAS\, Univ. of Kaiserslautern\, Germany) DTSTART:20210607T160000Z DTEND:20210607T170000Z DTSTAMP:20260404T094545Z UID:QM3/47 DESCRIPTION:Title: Topology of mixed states\nby Michael Fleischhauer (Dept. of Physic s & research center OPTIMAS\, Univ. of Kaiserslautern\, Germany) as part o f Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nTopological sta tes of matter have fascinated physicists since a long time. The notion of topology is however ususally associated with ground states of (many-body)- Hamiltonians\, which are pure. So what is left of it at finite temperature s and can topological protection be extended to non-equilibrium steady sta tes (NESS) of open systems? Can suitable observables be constructed that p reserve the integrity of topological invariants for mixed states and what are measurable consequences of their existence? Can we classify the topolo gy of finite-temperature and NESS using generalized symmetries? Motivated by topological charge pumps\, first introduced by Thouless\, I will first discuss a topological invariant for systems that break time reversal symme try based on the many-body polarization\, called ensemble geometric phase (EGP) [1]. In contrast to charge transport\, the EGP can be used to probe topology in one dimensional non-interacting [2] and interacting [3]\, clos ed and open systems alike. Furthermore different from other constructions\ , such as the Uhlmann phase\, it can be extended to two dimensions [4]. I will then extend the definition to systems with time-reversal symmetry and finally talk about measurable consequences of mixed-states topological in variants.\n\n[1] C.E. Bardyn\, L. Wawer\, A. Altland\, M. Fleischhauer\, S .Diehl\, (PRX 2018)\n\n[2] D. Linzner\, L. Wawer\, F. Grusdt\, M. Fleisch hauer\, (PRB 2016)\n\n[3] R. Unanyan\, M. Kiefer-Emmanouilidis\, M. Fleisc hhauer\, (PRL 2020)\n\n[4] L. Wawer\, M. Fleischhauer\, arxiv 2104.12115\n LOCATION:https://stable.researchseminars.org/talk/QM3/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Melotti (Université Paris Saclay) DTSTART:20210510T160000Z DTEND:20210510T170000Z DTSTAMP:20260404T094545Z UID:QM3/48 DESCRIPTION:Title: The free-fermion eight-vertex model via dimers\nby Paul Melotti (U niversité Paris Saclay) as part of Quantum Matter meets Maths (IST\, Lisb on)\n\n\nAbstract\nThe eight-vertex model is an useful description that ge neralizes several spin systems\, as well as the more common six-vertex mod el\, and others. In a special "free-fermion" regime\, it is known since th e work of Fan\, Lin\, Wu in the late 60s that the model can be mapped to n on-bipartite dimers. However\, no general theory is known for dimers in th e non-bipartite case\, contrary to the extensive rigorous description of G ibbs measures by Kenyon\, Okounkov\, Sheffield for bipartite dimers. In th is talk I will show how to transform these non-bipartite dimers into bipar tite ones\, on generic planar graphs. I will mention a few consequences: c omputation of long-range correlations\, criticality and critical exponents \, and their "exact" application to Z-invariant regimes on isoradial graph s.\n LOCATION:https://stable.researchseminars.org/talk/QM3/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Clement Delcamp (Max-Planck-Institute of Quantum Optics) DTSTART:20210614T160000Z DTEND:20210614T170000Z DTSTAMP:20260404T094545Z UID:QM3/49 DESCRIPTION:Title: On tensor network representations of the (3+1)d toric code\nby Cle ment Delcamp (Max-Planck-Institute of Quantum Optics) as part of Quantum M atter meets Maths (IST\, Lisbon)\n\n\nAbstract\nTensor network states prov ide a comprehensive framework for the analytic and numerical study of stro ngly correlated many-body systems. In recent years\, this framework has be en successfully applied to topological phases of matter. In this talk\, I will present two dual tensor network representations of the (3+1)d toric c ode ground state subspace\, which are obtained by initially imposing eithe r family of stabilizer constraints. I will discuss topological properties of the model from the point of view of these virtual symmetries\, demonstr ate that one of these representations is stable to all local tensor pertur bations---including those that do not map to local operators on the physic al Hilbert space---and explain\, both from a physical and category theoret ical viewpoint\, how the distinguishing properties of these representation s are related to the phenomenon of bulk-boundary correspondence.\n LOCATION:https://stable.researchseminars.org/talk/QM3/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Ákos Nagy (University of California\, Santa Barbara) DTSTART:20210705T160000Z DTEND:20210705T170000Z DTSTAMP:20260404T094545Z UID:QM3/50 DESCRIPTION:Title: Concentrating Majorana fermions\nby Ákos Nagy (University of Cali fornia\, Santa Barbara) as part of Quantum Matter meets Maths (IST\, Lisbo n)\n\n\nAbstract\nI will begin by defining a canonical family of perturbat ions of the Dirac equation. These perturbations are complex anti-linear\, thus ground states only form a real vector space. A special case of this t heory is known as the Jackiw–Rossi theory\, which models surface excitat ions on the surface of a topological insulator placed in proximity to an s -wave superconductor. While the physics of the theory is relatively well-u nderstood\, the mathematical side has not been studied\, even on surfaces\ , not to mention its generalizations to higher dimensional and on nontrivi al manifolds. I call these equations the ``generalized Jackiw–Rossi equa tions''.\n\nAfter the definitions and connections to physics\, I will pres ent my current work on the generalized Jackiw–Rossi equations. My main r esult is a concentration phenomenon which proves the physical expectation that such Majorana fermions concentrate around the vortices of the superco nducting order parameter. Moreover\, I provide approximate solutions that are exponentially sharp in the large coupling limit.\n\nIf time permits\, then I will show how these Majorana fermions define a bundle of projective spaces over the ``simple'' part of vortex moduli spaces. The holonomies o f such bundles give rise to projective representations of (surface) braid groups\, and thus\, speculatively\, can be of interest to quantum informat ion theorists.\n LOCATION:https://stable.researchseminars.org/talk/QM3/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Sven Bachmann (University of British Columbia) DTSTART:20210719T160000Z DTEND:20210719T170000Z DTSTAMP:20260404T094545Z UID:QM3/51 DESCRIPTION:Title: Adiabatic quantum transport\nby Sven Bachmann (University of Briti sh Columbia) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbs tract\nRecent years have seen much progress in the mathematical understand ing of quantum charge transport under slow driving\, in the presence of st rong interactions between the charge carriers. I will give an overview of recent results\, starting with the adiabatic theorem in an interacting set ting\, and continuing to topological transport where quantization can be s hown to be valid beyond the linear response setting.\n LOCATION:https://stable.researchseminars.org/talk/QM3/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Dung Xuan Nguyen (Brown University) DTSTART:20211122T170000Z DTEND:20211122T180000Z DTSTAMP:20260404T094545Z UID:QM3/52 DESCRIPTION:Title: Multiple Gravitons and spectral sum rules in Fractional Quantum Hall s ystems\nby Dung Xuan Nguyen (Brown University) as part of Quantum Matt er meets Maths (IST\, Lisbon)\n\n\nAbstract\nIn this talk\, I will provide the historical review of magneto-roton excitation\, which is the gapped n eutral excitation in the Lowest Landau Level. \nThe magneto-roton mode has spin-2 and can be considered as a massive graviton mode in 2+1D [1]. This spin-2 mode plays a central role in the physics of FQH. \nIn the current literature\, the spin-2 mode of Jain's sequences near filling fraction 1/2 can be thought of as the shear deformation of the composite fermion Fermi surface [2]. In this talk\, I will show that for Jain's sequences near fi lling fraction 1/4\, there will be an extra massive graviton mode [3]. The extra mode was proposed in our recent work on the Dirac composite fermion theory of general Jain's sequences in order to satisfy the Haldane bound of the static structure factor. The extra mode was confirmed numerically r ecently with the guidance of FQH sum rules [4]. I will briefly discuss our physical interpretation of the new massive graviton mode. If time allows\ , I will describe the experimental setup that can detect the graviton mode s [5]. \n\nReferences:\n\n[1] Siavash Golkar\, Dung X. Nguyen and Dam T. Son JHEP 021\, 01 (2016) \n\n[2] DX Nguyen\, A Gromov\, DT Son\, Physic al Review B 97 (19)\, 195103 (2018)\n\n[3] DX Nguyen\, DT Son\, arXiv:2105 .02092 (2021)\n\n[4] DX Nguyen\, Edward Rezayi\, Dam T. Son and Kun Yang To appeared (Arxiv:2111.xxxxx)\n\n[5] DX Nguyen\, DT Son\, Phys. Rev. Re search 3\, 023040 (2021)\n LOCATION:https://stable.researchseminars.org/talk/QM3/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Rosario Fazio (The Abdus Salam International Centre for Theoretica l Physics\, Trieste) DTSTART:20211018T160000Z DTEND:20211018T170000Z DTSTAMP:20260404T094545Z UID:QM3/53 DESCRIPTION:Title: Quantum time crystals\nby Rosario Fazio (The Abdus Salam Internati onal Centre for Theoretical Physics\, Trieste) as part of Quantum Matter m eets Maths (IST\, Lisbon)\n\n\nAbstract\nLandau's idea of classifying phas es of matter in terms of symmetry breaking is a cornerstone of modern phys ics. In his pioneering work Wilczek argued that an autonomous system can break time translation symmetry\, thus realising what he named as time cry stals. Their existence has been confirmed very recently in a number of exp eriments. I will briefly review the field focusing in particular on the so called Floquet time-crystals (arising in many-body systems that are perio dically driven) and on time-crystalline behaviour in quantum open systems. For this last case\, I will make connections to quantum synchronisation.\ n LOCATION:https://stable.researchseminars.org/talk/QM3/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Karol Życzkowski (Jagiellonian University Cracow\, Poland\; Cente r for Theoretical Physics\, PAS\, Warsaw) DTSTART:20211129T170000Z DTEND:20211129T180000Z DTSTAMP:20260404T094545Z UID:QM3/55 DESCRIPTION:Title: Multi-unitary matrices and their quantum applications\nby Karol Ż yczkowski (Jagiellonian University Cracow\, Poland\; Center for Theoretica l Physics\, PAS\, Warsaw) as part of Quantum Matter meets Maths (IST\, Lis bon)\n\n\nAbstract\nIn the space of bipartite unitary gates one distinguis hes the set of local gates\, formed by a tensor product\, $U=V_A \\otimes V_B$. Another distinguished set contains gates of extremal non-locality\, which maximize the entropy of entanglement defined by the operator Schmidt decomposition of a unitary gate $U$. If the reshuffled matrix\, $U^R$\, i s also unitary the matrix $U$ belongs to this class and is called dual uni tary. The matrix $S$ corresponding to the SWAP operation is strongly non-l ocal and dual unitary\, but it does not change entanglement of any state i t acts on. To describe creation of entanglement in the system one defines entangling power of a gate. Its absolute maximum is achieved for any dual unitary gate $U$\, such that its partial transpose $U^{\\Gamma}$ is also u nitary. These gates\, called two-unitary\, do not exist for dimension $d=2 ^2$\, but exist for $d=3^2$. We present an analytical construction of such a gate U of order $d=6^2=36$\, which leads to a solution of the quantum v ersion of the famous problem of $36$ officers of Euler [1]. It implies a p air of quantum orthogonal Latin squares of order six and an Absolutely Max imally Entangled (AME) state of four subsystems with six levels each. It e nables us to construct a quhex pure nonadditive quantum error detection co de useful to encode a 6-level state into a triple of such states. Using su ch a state one can teleport any unknown\, two-dice quantum state\, from an y pair of two subsystems to the lab possessing the two other dice forming the four-dice system. Our result imples that $2$-unitary gates exist for a ny squared dimension $d=N^2$ with $N\\ge 3$. A matrix $U$ of order $d=N^k$ is called k-unitary or multiunitary if it remains unitary after any of po ssible (2k choose k) reordering of the matrix. Any such a matrix leads to an AME state of $2k$ subsystems of size $N$. A simple example of a $3$-uni tary matrix $U$ of order $2^3=8$ corresponds to an AME(6\,2) state of six qubits.\n\nReferences:\n\n[1] S.A Rather\, A.Burchardt\, W. Bruzda\, G. Ra jchel-Mieldzioć\, A. Lakshminarayan and K. Życzkowski\, Thirty-six entan gled officers of Euler\, preprint arXiv:2104.05122\n LOCATION:https://stable.researchseminars.org/talk/QM3/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Cristiano Ciuti (Université de Paris\, CNRS\, Laboratoire Matéri aux et Phénomènes Quantiques\, France) DTSTART:20211220T170000Z DTEND:20211220T180000Z DTSTAMP:20260404T094545Z UID:QM3/56 DESCRIPTION:Title: Manipulating matter with vacuum fields: cavity-mediated transport in q uantum Hall systems\nby Cristiano Ciuti (Université de Paris\, CNRS\, Laboratoire Matériaux et Phénomènes Quantiques\, France) as part of Qu antum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nThe manipulation of matter by giant vacuum fields in electromagnetic resonators is an emergen t topic in physics and chemistry [1]. In this seminar\, after a general in troduction\, we will see how the cavity vacuum fluctuations can dramatical ly affect the physics of disordered quantum Hall systems. In particular\, we will show how\, in the presence of electronic disorder\, the cavity can mediate long-range electron hopping via the exchange of virtual photons\, involving both edge and bulk states [2]. Such an effect can produce a bre akdown of the topological protection of the integer quantum Hall effect as demonstrated in recent transport experiments [3]. Future perspectives wil l be discussed.\n\n[1] F. J. Garcia-Vidal\, C. Ciuti\, T. W. Ebbesen\, Man ipulating matter by strong coupling to vacuum fields\, Science 373\,178 (2 021).\n\n[2] C. Ciuti\, Cavity-mediated electron hopping in disordered qua ntum Hall systems\, Phys. Rev. B 104\, 155307 (2021).\n\n[3] F. Appugliese \, J. Enkner\, G. L. Paravicini-Bagliani\, M. Beck\, C. Reichl\, W. Wegsch eider\, G. Scalari\, C. Ciuti\, J. Faist\, Breakdown of the topological pr otection by cavity vacuum fields in the integer quantum Hall effect\, prep rint arXiv:2107.14145 (2021)\, to appear in\nScience.\n LOCATION:https://stable.researchseminars.org/talk/QM3/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Omri Golan (QEDMA Quantum Computing\, Israel) DTSTART:20211115T170000Z DTEND:20211115T180000Z DTSTAMP:20260404T094545Z UID:QM3/57 DESCRIPTION:Title: Geometric complexity in quantum matter: intrinsic sign problems in top ological phases\nby Omri Golan (QEDMA Quantum Computing\, Israel) as p art of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nThe infamo us sign problem leads to an exponential complexity in Monte Carlo simulati ons of generic many-body quantum systems. Nevertheless\, many phases of ma tter are known to admit a sign-problem-free representative\, allowing effi cient simulations on classical computers. Motivated by long standing open problems in many-body physics\, as well as fundamental questions in quantu m complexity\, the possibility of intrinsic sign problems\, where a phase of matter admits no sign-problem-free representative\, was recently raised but remains largely unexplored. I will describe results establishing the existence\, and the geometric origin\, of intrinsic sign problems in a bro ad class of topological phases in 2+1 dimensions. Within this class\, thes e results exclude the possibility of 'stoquastic' Hamiltonians for bosons\ , and of sign-problem-free determinantal Monte Carlo algorithms for fermio ns. The talk is based on Phys. Rev. Research 2\, 043032 and 033515.\n LOCATION:https://stable.researchseminars.org/talk/QM3/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Manfred Salmhofer (University of Heidelberg) DTSTART:20211025T160000Z DTEND:20211025T170000Z DTSTAMP:20260404T094545Z UID:QM3/58 DESCRIPTION:Title: Renormalization in condensed matter: Fermionic systems – from mathem atics to materials\nby Manfred Salmhofer (University of Heidelberg) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nI review the role of renormalization theory in many-fermion systems\, both from th e point of view of mathematical physics and that of applications to models of correlated electrons in solids. The Wilsonian renormalization group me thod allows for an unbiased analysis of competing ordering tendencies\, su ch as magnetism and superconductivity in effectively two-dimensional syste ms. As an example\, I will consider ferromagnetism and superconductivity i n the Hubbard model at Van Hove filling.\n LOCATION:https://stable.researchseminars.org/talk/QM3/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Predrag Cvitanović (Georgia Tech) DTSTART:20211206T170000Z DTEND:20211206T180000Z DTSTAMP:20260404T094545Z UID:QM3/59 DESCRIPTION:Title: Herding Cats: A Chaotic Field Theory\nby Predrag Cvitanović (Geor gia Tech) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstra ct\nSuppose you find yourself face-to-face with Young-Mills or Navier-Stok es or a nonlinear PDE or a funky metamaterial or a cloudy day. And you ask yourself\, is this thing "turbulent" What does that even mean?\n\nIf you were had a serious course on 'chaos'\, as Professor Ribeiro had\, you must have learned about the coin toss (Bernoulli map). I'll walk you through t his basic example of deterministic chaos\, than through the 'kicked rotor' \, a neat physical system that is chaotic\, and then put infinity of these together to explain what `chaos' or `turbulence' looks like in the spacet ime.\n\nWhat emerges is a spacetime which is very much like a big spring m attress that obeys the familiar continuum versions of a harmonic oscillato r\, the Helmholtz and Poisson equations\, but instead of being "springy"\, this metamaterial has an unstable rotor at every lattice site\, that give s\, rather than pushes back. We call this simplest of all chaotic field th eories the `spatiotemporal cat'. There is a QM^3 version\, ask Boris Gutki n or Tomaž Prosen to tell\nyou about it.\n\nIn the spatiotemporal formula tion of turbulence there is no evolution in time\, there are only a repert oires of admissible spatiotemporal patterns. In other words: throw away yo ur integrators\, and look for guidance in clouds' repeating patterns.\n\nT hat's `turbulence'. $\\href{https://www.youtube.com/watch?v=_JZom_gVfuw}{\ \text{And if you don't know\, now you know.}}$\n\n------------------------ ----\n\nNo actual cats\, graduate or undergraduate\, have shown interest i n\, or were harmed during this research.\n LOCATION:https://stable.researchseminars.org/talk/QM3/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Anton Kapustin (Caltech) DTSTART:20211213T170000Z DTEND:20211213T180000Z DTSTAMP:20260404T094545Z UID:QM3/60 DESCRIPTION:Title: Higher Berry classes for many-body quantum lattice systems\nby Ant on Kapustin (Caltech) as part of Quantum Matter meets Maths (IST\, Lisbon) \n\n\nAbstract\nM. Berry showed how to attach a line bundle and a connecti on on it to a family of quantum Hamiltonians with a non-degenerate ground state\, under the assumption that the Hilbert space is finite-dimensional. The first Chern class of this line bundle is a topological invariant of t he family. It is far from obvious if this construction can be generalized to quantum many-body Hamiltonians. Indeed\, naive generalizations fail be cause ground states of different Hamiltonians typically correspond to ineq uivalent representations of the algebra of observables. Nevertheless\, it is possible to construct such invariants by making use of a certain differ ential graded Lie algebra (DGLA) attached to a quantum lattice system. For example\, it turns out that to any family of gapped Hamiltonians on a 1d lattice one can attach a “quantized” degree-3 cohomology class on the parameter space. In this talk I will outline a construction of this DGLA a s well as the construction of higher Berry classes. The talk is based on a work in progress with Nikita Sopenko.\n LOCATION:https://stable.researchseminars.org/talk/QM3/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Dieter Mitsche (Université Jean Monnet\, France) DTSTART:20230220T140000Z DTEND:20230220T150000Z DTSTAMP:20260404T094545Z UID:QM3/61 DESCRIPTION:Title: Tail bounds for detection times in dynamic hyperbolic graphs\nby D ieter Mitsche (Université Jean Monnet\, France) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nMotivated by Krioukov et al's m odel of random hyperbolic graphs for real-world networks\, and inspired by the analysis of a dynamic model of graphs in Euclidean space by Peres et al.\, we introduce a dynamic model of hyperbolic graphs in which vertices are allowed to move according to a Brownian motion maintaining the distrib ution of vertices in hyperbolic space invariant. For different parameters of the speed of angular and radial motion\, we analyze tail bounds for det ection times of a fixed target and obtain a complete picture\, for very di fferent regimes\, of how and when the target is detected: as a function of the time passed\, we characterize the subset of the hyperbolic space wher e particles typically detecting the target are initially located. We overc ome several substantial technical difficulties not present in Euclidean sp ace\, and provide a complete picture on tail bounds. On the way\, we obtai n also new results for the time more general continuous processes with dri ft and reflecting barrier spent in certain regions\, and we also obtain im proved bounds for independent sums of Pareto random variables.\n\nJoint wo rk with Marcos Kiwi and Amitai Linker.\n LOCATION:https://stable.researchseminars.org/talk/QM3/61/ END:VEVENT END:VCALENDAR