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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

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.