AI Article Synopsis
- We refine the Affleck-Ludwig-Cardy formula for 1+1D conformal field theories, focusing on how high energy states relate to noninvertible global symmetries.
- We calculate the main contributions to the entanglement entropy for a system with noninvertible symmetries, specifically looking at a single interval.
- Using the critical double Ising model, we demonstrate that the ground state entanglement Hamiltonian exhibits a specific Hopf algebra symmetry when the system's boundary conditions reflect certain symmetries, and we provide the resulting symmetry-resolved entanglement entropies.
Article 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 subleading 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 entangling points 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.
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| http://dx.doi.org/10.1103/PhysRevLett.133.251602 | DOI Listing |
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