Entanglement bootstrap approach for gapped domain walls

TL;DR

This paper develops a theoretical framework for understanding gapped domain walls in topologically ordered systems, introducing new superselection sectors and entanglement measures to characterize their properties.

Contribution

It introduces the concept of parton superselection sectors and a systematic method to analyze their fusion and entanglement properties in gapped domain walls.

Findings

Defined the parton superselection sectors and their fusion rules.

Derived an exact expression for the topological entanglement entropy of gapped domain walls.

Extended entanglement axioms to systems with domain walls.

Abstract

We develop a theory of gapped domain wall between topologically ordered systems in two spatial dimensions. We find a new type of superselection sector -- referred to as the parton sector -- that subdivides the known superselection sectors localized on gapped domain walls. Moreover, we introduce and study the properties of composite superselection sectors that are made out of the parton sectors. We explain a systematic method to define these sectors, their fusion spaces, and their fusion rules, by deriving nontrivial identities relating their quantum dimensions and fusion multiplicities. We propose a set of axioms regarding the ground state entanglement entropy of systems that can host gapped domain walls, generalizing the bulk axioms proposed in [B. Shi, K. Kato, and I. H. Kim, Ann. Phys. 418, 168164 (2020)]. Similar to our analysis in the bulk, we derive our main results by examining the self-consistency relations of an object called information convex set. As an application, we define an analog of topological entanglement entropy for gapped domain walls and derive its exact expression.