The topology and geometry of the space of gapped lattice systems
Speaker: Anton Kapustin
Date: Wed, Dec 9, 2020
Location: PIMS, University of Saskachewan, Zoom
Conference: quanTA CRG Seminar
Subject: Mathematics, Physics, Condensed Matter and Statistical Mechanics, Particle Physics and Quantum Field Theory
Class: Scientific
CRG: Quantum Topology and its Applications
Date: Wed, Dec 9, 2020
Location: PIMS, University of Saskachewan, Zoom
Conference: quanTA CRG Seminar
Subject: Mathematics, Physics, Condensed Matter and Statistical Mechanics, Particle Physics and Quantum Field Theory
Class: Scientific
CRG: Quantum Topology and its Applications
Abstract:
Recently there has been a lot of progress in classifying phases of gapped quantum many-body systems. From the mathematical viewpoint, a phase of a quantum system is a connected component of the “space” of gapped quantum systems, and it is natural to study the topology of this space. I will explain how to probe it using generalizations of the Berry curvature. I will focus on the case of lattice systems where all constructions can be made rigorous. Coarse geometry plays an important role in these constructions.
