Fermion decoration construction of symmetry protected trivial orders for fermion systems with any symmetries G_f and in any dimensions

2018/09/04 by Tian Lan, Chenchang Zhu, Xiao-Gang Wen
Physics and Astronomy · #cond-mat.str-el

paper · pdf · doi:10.1103/physrevb.100.235141

published as Phys. Rev. B 100, 235141 (2019) · 46 pages, 6 figures

arxiv created 2018/09/04 · arxiv updated 2020/01/01

Abstract

We use higher dimensional bosonization and fermion decoration to construct exactly soluble interacting fermion models to realize fermionic symmetry protected trivial (SPT) orders (which are also known as symmetry protected topological orders) in any dimensions and for generic fermion symmetries G_f, which can be a non-trivial Z₂^f extension (where Z₂^f is the fermion-number-parity symmetry). This generalizes the previous results from group superconhomology of Gu and Wen (arXiv:1201.2648), where G_f is assumed to be a trivial Z₂^f extension. We find that the SPT phases from fermion decoration construction can be described in a compact way using higher groups.

Citations

• Symmetry-protected topological orders for interacting fermions -- Fermionic topological nonlinear σ models and a special group supercohomology theory