Tensor network representations of fermionic crystalline topological phases on two-dimensional lattices

TL;DR

This paper develops tensor network (PEPS) representations for 2D fermionic crystalline SPT phases, enabling classification of these phases protected by wallpaper group symmetries for both spinless and spin-1/2 fermions.

Contribution

It introduces a PEPS-based framework to construct and classify 2D fermionic crystalline SPT phases with wallpaper group symmetries.

Findings

PEPS representations for 2D fermionic SPT phases

Full classification of 2D crystalline fSPT phases with wallpaper groups

Framework applicable to both spinless and spin-1/2 fermions

Abstract

We investigate the tensor network representations of fermionic crystalline symmetry-protected topological (SPT) phases on two-dimensional lattices. As a mapping from virtual indices to physical indices, projected entangled-pair state (PEPS) serves as a concrete way to construct the wavefunctions of 2D crystalline fermionic SPT (fSPT) phases protected by 17 wallpaper group symmetries, for both spinless and spin-1/2 fermions. Based on PEPS, the full classification of 2D crystalline fSPT phases with wallpaper groups can be obtained. Tensor network states provide a natural framework for studying 2D crystalline fSPT phases.