A K matrix Construction of Symmetry Enriched Phases of Matter

TL;DR

This paper constructs explicit models of symmetry enriched topological phases using the K matrix formalism, revealing how symmetries influence edge modes and anyon structures in Abelian and non-chiral systems.

Contribution

It provides concrete K matrix examples of symmetry enriched phases, illustrating the role of symmetry in topological order and edge mode protection, including exotic anyon behaviors.

Findings

Symmetry determines the existence of protected gapless edge modes.

Examples include phases with charge fractionalization.

Identification of group extension structures in symmetry-enriched phases.

Abstract

We construct in the K matrix formalism concrete examples of symmetry enriched topological phases, namely intrinsically topological phases with global symmetries. We focus on the Abelian and non-chiral topological phases and demonstrate by our examples how the interplay between the global symmetry and the fusion algebra of the anyons of a topologically ordered system determines the existence of gapless edge modes protected by the symmetry and that a (quasi)-group structure can be defined among these phases. Our examples include phases that display charge fractionalization and more exotic non-local anyon exchange under global symmetry that correspond to general group extensions of the global symmetry group.