researchseminars.org

Anton Kapustin (Caltech)
2021-04-27 15:00 - 16:00 UTC | https://stable.researchseminars.org/talk/IHES-Quantum-Encounters/1/
Title: Noncommutative geometry of quantum lattice models and the higher Berry phase (https://stable.researchseminars.org/talk/IHES-Quantum-Encounters/1/)
by Anton Kapustin (Caltech) as part of IHES Quantum Encounters

Abstract
Recently methods of quantum statistical mechanics have been fruitfully applied to the study of phases of quantum lattice systems at zero temperature. For example, a rigorous definition of a Short-Range Entangled phase of matter has been given and a classification of such phases in one spatial dimension has been achieved. I will discuss some of these developments, focusing on the topology and geometry of the space of Short-Range Entangled states. According to a conjecture of A. Kitaev, these spaces form a loop spectrum in the sense of homotopy theory. This conjecture implies that to any family of Short-Range entangled states in one dimension one can associate a gerbe on the parameter space. I will show how to construct such a gerbe. Thе curvature of this gerbe is a closed 3-form with quantized periods and can be regarded as a higher-dimensional generalization of the curvature of the Berry connection.

See seminar webpage https://seminars.ihes.fr/quantum/ for the zoom link

Peter C.W. Holdsworth (Ecole Normale Supérieure de Lyon)
2021-06-01 14:00 - 15:00 | https://stable.researchseminars.org/talk/IHES-Quantum-Encounters/2/
Title: Emergence: from spins to charges (https://stable.researchseminars.org/talk/IHES-Quantum-Encounters/2/)
by Peter C.W. Holdsworth (Ecole Normale Supérieure de Lyon) as part of IHES Quantum Encounters

Abstract
Emergence is a major buzz word of our times. My working definition, which gives plenty of room for manoeuvre is: the appearance of many body phenomena of higher symmetry than that of the Hamiltonian and degrees of freedom at the microscopic level.

In this colloquium I will discuss a topical example - the frustrated magnetic material, spin ice. Here, to an excellent approximation a classical field theoretic description with continuous U(1) symmetry emerges from Ising like degrees of freedom. The associated quasi-particles appear to be freely moving magnetic charge - magnetic monopoles - and the system behaves as a magnetic Coulomb fluid in the grand canonical ensemble with intrinsic topological properties. With the addition of quantum fluctuations the emergent magneto-statics develops further into a complete analogue of quantum electrodynamics. I will aliment this discussion with experimental results from a wide range of systems.

See the zoom link at https://indico.math.cnrs.fr/event/6687/
