Non-abelian bosonization of fermion symmetry-protected topological states

TL;DR

This paper develops a non-abelian bosonization framework for free fermion symmetry-protected topological states, unifying fermionic and bosonic descriptions via topological sigma models with phase transitions.

Contribution

It introduces a non-abelian bosonization approach that maps fermionic SPTs to non-linear sigma models with topological terms, connecting different topological phases.

Findings

Bosonization maps fermionic SPTs to sigma models with $ heta$ term.

Phase transitions occur as $ heta$ varies from 0 to 2π.

Extension to higher-dimensional spin SPTs and critical spin liquids.

Abstract

Applying the results of Ref.[1], we carry out the non-abelian bosonization for a class of free fermion symmetry-protected topological states (SPTs). The resulting boson theories are non-linear sigma models with topological $\theta$ term, thus unifying the field theory description of the (free) fermionic and bosonic SPTs. Tuning $\theta$ from $0$ to $2\pi$ triggers the topological trivial to non-trivial phase transitions. In addition, applying the same idea to the symmetry-protected critical spin liquids, we obtain the NL$\s$ models for spin SPTs living in one spatial dimension higher.