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Entanglement bootstrap approach for gapped domain walls
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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.
Forward citations
Cited by 2 Pith papers
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A systematic search for conformal field theories in very small spaces
A symmetry-free entropy search on four-site states recovers known CFTs and yields unclassified candidate CFTs with 1<c<2.
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An Algebraic Theory of Gapped Domain Wall Partons
Parton sectors on gapped domain walls are identified with indecomposable bimodule subcategories of relative tensor products, giving a categorical theory with a proven dimension formula.
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