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Anomalies on the Lattice, Homotopy of Quantum Cellular Automata, and a Spectrum of Invertible States
Alexander M. Czajka, Roman Geiko, Ryan Thorngren·December 1, 2025
cond-mat.str-elhep-thMathematical PhysicsQuantum Physics
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Abstract
We develop a rigorous topological theory of anomalies on the lattice, which are obstructions to gauging global symmetries and the existence of trivial symmetric states. We also construct $Ω$-spectra of a class of invertible states and quantum cellular automata, which allows us to classify both anomalies and symmetry protected topological phases up to blend equivalence.