Topological Phases of Quantum Lattice Systems and Higher Berry Classes - Lecture 3

Delve into recent advancements in defining the space of gapped lattice systems and their implications for classifying gapped phases of matter in this comprehensive lecture. Explore the evolution of beliefs surrounding the classification of these phases, from the initial assumption of Topological Quantum Field Theory (TQFT) to the current understanding of Short-Range Entangled (SRE) phases and their potential relation to invertible TQFT. Examine the cobordism conjecture and its suggestion that SRE phases are classified by the homotopy groups of a certain Omega-spectrum. Discover how this implies that infinite-dimensional spaces of SRE systems carry cohomology classes generalizing the Berry curvature. Learn about the construction of "higher Berry classes" and their equivariant versions, including the Hall conductance and its nonabelian analogs. Gain insight into the key ingredient of this construction: a differential graded Frechet-Lie algebra attached to any infinite-volume lattice system. Join Anton Kapustin from Caltech for this 1 hour and 46 minute lecture, part of a series presented at the Institut des Hautes Etudes Scientifiques (IHES), as he unravels the complexities of topological phases in quantum lattice systems.