Anomalies on the Lattice, Homotopy of Quantum Cellular Automata, and a Spectrum of Invertible States

• URL: http://arxiv.org/abs/2512.02105v1
• Date: Mon, 01 Dec 2025 19:00:01 GMT
• Title: Anomalies on the Lattice, Homotopy of Quantum Cellular Automata, and a Spectrum of Invertible States
• Authors: Alexander M. Czajka, Roman Geiko, Ryan Thorngren,
• Abstract summary: We develop a rigorous theory of anomalies on the lattice, which are obstructions to gauging global symmetries and the existence of trivial symmetric states.<n>We also construct $$-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.
• Score: 41.99844472131922
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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