Failure of the Crystalline Equivalence Principle for Weak Free Fermions

2024/08/13 by Daniel Sheinbaum, Sheinbaum, Daniel, Antolín-Camarena, Omar · 2 citations
Engineering · Materials Science · Physics and Astronomy · #Advanced Materials Characterization Techniques #FOS: Physical sciences #Machine Learning in Materials Science #Mathematical Physics (math-ph) #Strongly Correlated Electrons (cond-mat.str-el) #Surface and Thin Film Phenomena

paper · pdf · doi:10.48550/arxiv.2408.07203

openalex publication_date 2024/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Interacting crystalline SPT phases were first classified by Thorngren and Else through the crystalline equivalence principle, suggesting that a spatial group symmetry can be treated as if it were an internal symmetry group. Using techniques from topology we elucidate how this principle holds for one of the proposals for the interacting bosonic case and yet fails for weak free fermion phases. Last we show how a variant of the principle does hold for strong crystalline free fermion phases, showing that it is not necessary for the cohomology theory to be of Borel type.

Cited by

• Weak in the boundary: How weak SPT phases spoil anomaly matching
• Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence

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