Entanglement bootstrap approach for gapped 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.

42 pages, 54 figures

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Cited by in corpus (15)

• Chiral central charge from a single bulk wave function
• Modular commutator in gapped quantum many-body systems
• Towards Non-Invertible Anomalies from Generalized Ising Models
• Mixed-State Entanglement Measures in Topological Order
• Nonlocal growth of quantum conditional mutual information under decoherence
• Symmetry Fractionalized (Irrationalized) Fusion Rules and Two Domain-Wall Verlinde Formulae
• Entropy scaling law and the quantum marginal problem
• Stability of topological purity under random local unitaries
• Chiral Virasoro algebra from a single wavefunction
• Conformal geometry from entanglement
• Remote detectability from entanglement bootstrap I: Kirby's torus trick
• Immersed figure-8 annuli and anyons
• Knots and entanglement
• Universal Decay of Mutual Information and Conditional Mutual Information in Gapped Pure- and Mixed-State Quantum Matter
• $C^{\ast }$-categorical prefactorization algebras for superselection sectors and topological order