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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-ph2024
Quantization of the higher Berry curvature and the higher Thouless pump
Adam Artymowicz, Anton Kapustin, Nikita Sopenko
We show that for families of 1d lattice systems in an invertible phase, the cohomology class of the higher Berry curvature can be refined to an integral degree-3 class on the param…