A theory of topological edges and domain walls

TL;DR

The paper develops a general framework for analyzing domain walls between 2D topologically ordered phases using topological symmetry breaking via boson condensation in overlapped layered systems, yielding a condensed intermediate theory $T$ that encodes boundary and bulk excitations. By examining branching and fusion in the $T$-theory, the authors predict which excitations can pass through interfaces, which become confined to walls, and how edge spectra and transport arise from the residual bulk theory $C_2$. They illustrate the method with two concrete setups: a toric-code island in an Ising/MR-like medium (Kitaev honeycomb context) and a Pfaffian MR–NASS interface, showing precise identifications between bulk anyons, boundary excitations, and wall modes. The framework provides a systematic route to analyze domain walls in layered topological systems and connects to coset constructions and simple-current condensates, enabling broad applicability to quantum Hall and lattice-model interfaces.

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.

Figures (1)

• Figure 1: Side view of two overlapping layers supporting topological phases I and III. If we bring the layers close together, a condensate may form in the overlap region leading to a phase II. The theory T on the left boundary describes excitations that can be divided into bulk excitations of phase I and of phase II, and excitations that only can propagate along the boundary. On the right boundary a similar situation occurs for the same theory T, now with III replacing I. The subset of T excitations that are strictly confined to the left and right boundaries are therefore different in general.