- Letter
Failure of the crystalline equivalence principle for weak free fermions
Phys. Rev. B 111, L081118 – Published 27 February, 2025
DOI: https://doi.org/10.1103/PhysRevB.111.L081118
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. Lastly, 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.
