Noninvertible Symmetry-Resolved Affleck-Ludwig-Cardy Formula and Entanglement Entropy from the Boundary Tube Algebra

2024/09/04 by Yichul Choi, Brandon C. Rayhaun, Choi, Yichul +3 · 6 citations
Computer Science · Physics and Astronomy · #Matrix Theory and Algorithms #Quantum and Classical Electrodynamics

paper · pdf · doi:10.48550/arxiv.2409.02806

Abstract

We derive a refined version of the Affleck-Ludwig-Cardy formula for a 1+1d conformal field theory, which controls the asymptotic density of high energy states on an interval transforming under a given representation of a noninvertible global symmetry. We use this to determine the universal leading and sub-leading contributions to the noninvertible symmetry-resolved entanglement entropy of a single interval. As a concrete example, we show that the ground state entanglement Hamiltonian for a single interval in the critical double Ising model enjoys a Kac-Paljutkin H₈ Hopf algebra symmetry when the boundary conditions at the entanglement cuts are chosen to preserve the product of two Kramers-Wannier symmetries, and we present the corresponding symmetry-resolved entanglement entropies. Our analysis utilizes recent developments in symmetry topological field theories (SymTFTs).

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