Noninvertible Symmetry-Resolved Affleck-Ludwig-Cardy Formula and Entanglement Entropy from the Boundary Tube Algebra
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| Format: | Preprint |
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2024
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| _version_ | 1866909883599683584 |
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| author | Choi, Yichul Rayhaun, Brandon C. Zheng, Yunqin |
| author_facet | Choi, Yichul Rayhaun, Brandon C. Zheng, Yunqin |
| contents | 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). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_02806 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Noninvertible Symmetry-Resolved Affleck-Ludwig-Cardy Formula and Entanglement Entropy from the Boundary Tube Algebra Choi, Yichul Rayhaun, Brandon C. Zheng, Yunqin High Energy Physics - Theory Strongly Correlated Electrons Quantum Algebra Quantum Physics 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). |
| title | Noninvertible Symmetry-Resolved Affleck-Ludwig-Cardy Formula and Entanglement Entropy from the Boundary Tube Algebra |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Quantum Algebra Quantum Physics |
| url | https://arxiv.org/abs/2409.02806 |