Topological invariants of gapped states and cosheaves on sites

Abstract: Recently, an approach to constructing topological invariants of gapped ground-states of lattice systems has been developed in our joint work with N. Sopenko. It applies to arbitrary gapped states of infinite-volume lattice spin systems with rapidly decaying interactions and employs C*-algebraic techniques. In this talk, I will explain an interpretation of these invariants as obstructions to gauging, i.e. to promoting a symmetry to a local symmetry. The key observation is that locality on a lattice is an asymptotic notion sensitive only to the large-scale geometry of the support set. Following Kashiwara and Schapira, one can encode locality using a natural Grothendieck topology on a category of semilinear subsets of Eucludean space. Infinitesimal symmetries of a gapped state form a cosheaf over the corresponding site, and the topological invariants are encoded in its Cech complex.

mathematical physicsalgebraic topologycategory theoryquantum algebra

Audience: researchers in the topic

Topological Quantum Field Theory Club (IST, Lisbon)

Series comments: To receive the series announcements, which include the Zoom access password*, please register in
math.tecnico.ulisboa.pt/seminars/tqft/index.php?action=subscribe#subscribe
*the last announcement for a seminar is sent 2 hours before the seminar.
TQFT Club video channel: educast.fccn.pt/vod/channels/k0rk5qewc?locale=en