Anyonic symmetry fractionalization in SET phases

TL;DR

This paper investigates symmetry fractionalization in symmetry enriched topological phases, introducing a phase that characterizes how anyons carry fractional symmetry quantum numbers without permutation effects.

Contribution

It proposes a framework for understanding symmetry fractionalization in SET phases under assumptions that exclude anyon permutation effects.

Findings

Defines a phase for symmetry fractionalization in SET phases

Provides a theoretical framework for analyzing symmetry actions on anyons

Clarifies conditions under which symmetry acts without permuting anyons

Abstract

We consider the anyonic spin systems with a global symmetry, the so-called symmetry enriched topological (SET) phases. We introduce the phase characterizing the symmetry fractionalization of the anyons. Our assumptions on how the global symmetry acts prevents anyon permutation effects.