• Corpus ID: 231839704

Invertible phases for mixed spatial symmetries and the fermionic crystalline equivalence principle

@inproceedings{Debray2021InvertiblePF,
  title={Invertible phases for mixed spatial symmetries and the fermionic crystalline equivalence principle},
  author={Arun Debray},
  year={2021}
}

• A. Debray
• Published 5 February 2021
• Mathematics

Freed-Hopkins give a mathematical ansatz for classifying gapped invertible phases of matter with a spatial symmetry in terms of Borel-equivariant generalized homology. We propose a slight generalization of this ansatz to account for cases where the symmetry type mixes nontrivially with the spatial symmetry, such as crystalline phases with spin-1/2 fermions. From this ansatz, we prove as a theorem a"fermionic crystalline equivalence principle,"as predicted in the physics literature. Using this and the Adams spectral sequence, we compute classifications of some classes of phases with a point group symmetry; in cases where these phases have been studied by other methods, our results agree with the literature.