A theory of topological edges and domain walls

TL;DR

This paper develops a general theoretical framework to understand the degrees of freedom, edge excitations, and transport properties of domain walls between different topologically ordered phases in two dimensions.

Contribution

It introduces a unified approach based on topological symmetry breaking to analyze domain walls in various topological phases, including Kitaev's model and fractional quantum Hall states.

Findings

Predicted spectrum of edge excitations for various domain walls

Analyzed transport properties across topological domain walls

Applied framework to both Abelian and non-Abelian phases

Abstract

We investigate domain walls between topologically ordered phases in two spatial dimensions and present a simple but general framework from which their degrees of freedom can be understood. The approach we present exploits the results on topological symmetry breaking that we have introduced and presented elsewhere. After summarizing the method, we work out predictions for the spectrum of edge excitations and for the transport through edges in some representative examples. These include domain walls between the Abelian and non-Abelian topological phases of Kitaev's honeycomb lattice model in a magnetic field, as well as recently proposed domain walls between spin polarized and unpolarized non-Abelian fractional quantum Hall states at different filling fractions.