17 citations · 26 across the 8 of their papers we have counts for
4 papers · 1 filter
Anomalies, higher symmetries, and homotopy theory I: crossed precosheaves and a nonabelian Cech construction
Anton Kapustin, Shixiong Xu
Symmetries of a quantum field theory or a quantum lattice model are expected to be described not by a group but by a homotopy type, whose homotopy groups are the higher symmetry gr…
Higher symmetries and anomalies in quantum lattice systems
Anton Kapustin, Shixiong Xu
We define an 't Hooft anomaly index for a group acting on a 2d quantum lattice system by finite-depth circuits. It takes values in the degree-4 cohomology of the group and is an ob…
A mathematical theory of topological invariants of quantum lattice systems
Adam Artymowicz, Anton Kapustin, Bowen Yang
We show that Hall conductance and its non-abelian and higher-dimensional analogs are obstructions to promoting a symmetry of a state to a gauge symmetry. To do this, we define a lo…
Anomalous symmetries of quantum spin chains and a generalization of the Lieb-Schultz-Mattis theorem
Anton Kapustin, Nikita Sopenko
For any locality-preserving action of a group on a quantum spin chain one can define an anomaly index taking values in the group cohomology of . The anomaly index is a kinem…