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

• URL: http://arxiv.org/abs/2409.02806v2
• Date: Wed, 04 Dec 2024 20:23:22 GMT
• Title: Noninvertible Symmetry-Resolved Affleck-Ludwig-Cardy Formula and Entanglement Entropy from the Boundary Tube Algebra
• Authors: Yichul Choi, Brandon C. Rayhaun, Yunqin Zheng,
• Abstract summary: We derive a refined version of the Affleck-Ludwig-Cardy formula for a 1+1d conformal field theory. We use this to determine the universal leading and sub-leading contributions to the noninvertible symmetry-resolved entanglement entropy of a single interval.
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• 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 $H_8$ 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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