BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Amanda Young (Techincal University of Munich) DTSTART:20211011T160500Z DTEND:20211011T165000Z DTSTAMP:20260404T060944Z UID:BIRS-21w5502/1 DESCRIPTION:Title: A bulk gap in the presence of edge states for a Haldane pseudo potential\nby Amanda Young (Techincal University of Munich) as part of BIRS workshop: Topology and Entanglement in Many-Body Systems\n\n\nAbstra ct\nIn this talk\, we discuss a recent result on a bulk gap for a truncate d Haldane pseudopotential with maximal half filling\, which describes a st rongly correlated system of spinless bosons in a cylinder geometry. For th is Hamiltonian with either open or periodic boundary conditions\, we prove a spectral gap above the highly degenerate ground-state space which is un iform in the volume and particle number. Our proofs rely on identifying in variant subspaces to which we apply gap-estimate methods previously develo ped only for quantum spin Hamiltonians. In the case of open boundary condi tions\, the lower bound on the spectral gap accurately reflects the presen ce of edge states\, which do not persist into the bulk. Customizing the ga p technique to the invariant subspace\, we avoid the edge states and estab lish a more precise estimate on the bulk gap in the case of periodic bound ary conditions. The same approach can also be applied to prove a bulk gap for the analogously truncated 1/3-filled Haldane pseudopotential for the f ractional quantum Hall effect.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5502/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Anurag Anshu (UC Berkeley) DTSTART:20211011T173000Z DTEND:20211011T181500Z DTSTAMP:20260404T060944Z UID:BIRS-21w5502/2 DESCRIPTION:Title: An area law for ground states of 2D frustration-free spin syst ems\nby Anurag Anshu (UC Berkeley) as part of BIRS workshop: Topology and Entanglement in Many-Body Systems\n\n\nAbstract\nWe will discuss an ar ea law for ground states of locally gapped frustration-free 2D lattice spi n systems. We first generalize the optimal approximation of the boolean AN D function to a non-commuting setting\, showing that the ground state proj ector of a locally gapped frustration-free 1D spin system can be optimally approximated in a similar manner. For 2D spin systems we then construct a n approximate ground state projector (AGSP) that employs the optimal 1D ap proximation along the boundary of the bipartition of interest. If time per mits\, we will also discuss the challenges in extending the proof to 3D sy stems. Joint work with Itai Arad and David Gosset (https://arxiv.org/abs/2 103.02492).\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5502/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Yoshiko Ogata (The University of Tokyo) DTSTART:20211012T233000Z DTEND:20211013T001500Z DTSTAMP:20260404T060944Z UID:BIRS-21w5502/3 DESCRIPTION:Title: Classification of SPT phases\nby Yoshiko Ogata (The Univer sity of Tokyo) as part of BIRS workshop: Topology and Entanglement in Many -Body Systems\n\n\nAbstract\nI will talk about our trial on classification of SPT phases in quantum statistical mechanics.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5502/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Kohtaro Kato (Nagoya University) DTSTART:20211013T010000Z DTEND:20211013T014500Z DTSTAMP:20260404T060944Z UID:BIRS-21w5502/4 DESCRIPTION:Title: Entanglement bootstrap approach in 2D gapped spin systems\ nby Kohtaro Kato (Nagoya University) as part of BIRS workshop: Topology an d Entanglement in Many-Body Systems\n\n\nAbstract\nQuantum phases (without symmetry) in two-dimensional (2D) gapped systems are expected to be class ified into different topologically ordered phases\, which cannot be descri bed by the conventional theory of symmetry-breaking. A vast amount of work has been dedicated to classify/characterize these new phases\, and nowada ys\, it is widely believed that all topologically ordered phases can be cl assified by topological quantum field theory (TQFT). Although the existing analytical studies as well as numerical studies are consistent with the p rediction of this theory\, we still lack a general\, concrete proof that d irectly shows that any 2D gapped quantum phases should be classified in th is framework. \n\nIn this talk\, we propose the entanglement bootstrap pr ogram to make progress on this important problem. In this program\, we pos it that local reduced density matrices of such systems obey a set of entro pic identities followed by the area law of entanglement. We show that the axioms of the fusion rules of anyon are derived from the entropic identiti es only. We then discuss recent applications of this approach to S-matrix and central charges. We also discuss an obstacle of the universality of th is approach\, spurious topological entropy.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5502/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Bruno Nachtergaele (University of California\, Davis) DTSTART:20211013T160000Z DTEND:20211013T164500Z DTSTAMP:20260404T060944Z UID:BIRS-21w5502/5 DESCRIPTION:Title: Spectral gaps\, gapped curves\, and stability\nby Bruno Na chtergaele (University of California\, Davis) as part of BIRS workshop: To pology and Entanglement in Many-Body Systems\n\n\nAbstract\nI discuss the stability of spectral gaps for quantum lattice systems subject to small pe rturbations of the interactions defining the Hamiltonian and its connectio n to topological and symmetry-protected topological phases. I will review the current status of the problem and then discuss the application of rece nt results to the stability of a dimerized phases in a family of quantum s pin chains with O(n) symmetry and certain features of their phase diagram\ , including in the neighborhood of a non-frustration-free point. (Includes joint work with Robert Sims and Amanda Young and with Jakob Bjoernberg\, Peter Muehlbacher\, and Daniel Ueltschi).\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5502/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Levin (University of Chicago) DTSTART:20211013T173000Z DTEND:20211013T181500Z DTSTAMP:20260404T060944Z UID:BIRS-21w5502/6 DESCRIPTION:Title: Stability of ground state degeneracy to long-range interaction s\nby Michael Levin (University of Chicago) as part of BIRS workshop: Topology and Entanglement in Many-Body Systems\n\n\nAbstract\nSome gapped quantum many-body systems have the interesting property that they have mul tiple nearly degenerate ground states with an energy splitting that is exp onentially small in the system size. Furthermore\, this nearly exact degen eracy is a robust phenomenon in the sense that it does not require fine tu ning parameters in the Hamiltonian. While this kind of nearly exact ground state degeneracy is a well-established phenomenon for systems with short- range interactions\, much less is known about long-range interactions (e.g .\, power-law decaying interactions). In this talk\, I will present a rigo rous result showing that a robust\, exponentially small ground state split ting also occurs in some models with long-range interactions.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5502/6/ END:VEVENT BEGIN:VEVENT SUMMARY:David Pérez-García (Complutense University of Madrid - ICMAT) DTSTART:20211014T160000Z DTEND:20211014T164500Z DTSTAMP:20260404T060944Z UID:BIRS-21w5502/7 DESCRIPTION:Title: Bulk-boundary correspondence in Tensor Networks\nby David Pérez-García (Complutense University of Madrid - ICMAT) as part of BIRS workshop: Topology and Entanglement in Many-Body Systems\n\n\nAbstract\nTe nsor Networks constitute a very rich family of states that is known to cap ture the low energy sector of locally interacting quantum systems. One of their most interesting features is the existence of a rigorous bulk-bounda ry correspondence: interesting (and usually complex) bulk properties have an easier characterization at the boundary. Examples of such bulk properti es include the existence of a spectral gap or the presence of topological order. Both can be combined to shed new light in the problem of the existe nce of self-correcting quantum memories in 2D.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5502/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Jeongwan Haah (Microsoft Research) DTSTART:20211014T173000Z DTEND:20211014T181500Z DTSTAMP:20260404T060944Z UID:BIRS-21w5502/8 DESCRIPTION:Title: Gapping out a subalgebra and classifying Clifford QCAs\nby Jeongwan Haah (Microsoft Research) as part of BIRS workshop: Topology and Entanglement in Many-Body Systems\n\n\nAbstract\nA QCA is a locality pres erving automorphism of operator algebra on lattices. Such an automorphism is characterized by a subalgebra on a boundary. The existence of a maximal commutative set of local operators within the subalgebra restricts feasib le QCAs. From this approach\, we classify Clifford QCA in 3d\, the ones th at map every Pauli operator to another.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5502/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Walter (University of Amsterdam) DTSTART:20211015T160000Z DTEND:20211015T164500Z DTSTAMP:20260404T060944Z UID:BIRS-21w5502/9 DESCRIPTION:Title: Approximate QCAs and a converse to the Lieb-Robinson bounds\nby Michael Walter (University of Amsterdam) as part of BIRS workshop: T opology and Entanglement in Many-Body Systems\n\n\nAbstract\nUnitary evolu tions of quantum lattice systems that preserve locality are called "quantu m cellular automata"\, or QCAs. QCAs in one dimension have been completely classified by an index theory. However\, physical systems often only pres erve locality approximately. For example\, Hamiltonian evolutions on the l attice satisfy Lieb-Robinson bounds rather than strict locality. In this t alk\, we will discuss QCAs that approximately preserve locality. As we wil l see\, the index theory of 1D QCAs is robust even when considering these more general evolutions. As a consequence\, we also obtain a converse to t he Lieb-Robinson bounds in one dimension. Based on work with Daniel Ranard and Freek Witteveen in arXiv:2012.00741.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5502/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Nikita Sopenko (Caltech) DTSTART:20211015T173000Z DTEND:20211015T181500Z DTSTAMP:20260404T060944Z UID:BIRS-21w5502/10 DESCRIPTION:Title: Invariants for families of gapped ground states\nby Nikit a Sopenko (Caltech) as part of BIRS workshop: Topology and Entanglement in Many-Body Systems\n\n\nAbstract\nI will talk about how to define invarian ts for families of d-dimensional gapped ground states on the lattice known as Higher Berry classes. As an application I will show how to construct t he invariant of 2d gapped ground states with semisimple Lie group symmetry G taking values in H^3(G\,R) and show it’s quantization for invertible states.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5502/10/ END:VEVENT END:VCALENDAR