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math-ph2026
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…
math-ph2025
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…