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arXiv · 2607.28811

Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence

Daniel Sheinbaum·Omar Antolín-Camarena
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Abstract

Freed and Hopkins developed an ansatz for classifying interacting SPT phases using invertible field theories with a natural Free to Interacting (FTI) map from free fermion phases. This ansatz has been generalized to include crystalline phases and a crystalline equivalence principle (CEP). However, motivated by failure of the CEP for weak free fermions and the FTI, here we generalize the original Freed and Hopkins ansatz to a fully equivariant version for symmorphic crystallographic symmetries and show there is a natural equivariant FTI map from symmorphic crystalline weak free fermions. We further discuss why this equivariant ansatz is both mathematically and physically more natural than the spatial symmetry extension by Freed and Hopkins and why full equivariance should hold over the CEP.

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Daniel Sheinbaum, Omar Antolín-Camarena. 2026-07-30. Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence. https://arxiv.org/abs/2607.28811

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