A Non-Invertible Symmetry-Resolved Affleck-Ludwig-Cardy Formula and Entanglement Entropy from the Boundary Tube Algebra

• URL: http://arxiv.org/abs/2409.02806v1
• Date: Wed, 4 Sep 2024 15:25:05 GMT
• Title: A Non-Invertible 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 non-invertible symmetry-resolved entanglement entropy of a single interval.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 non-invertible global symmetry. We use this to determine the universal leading and sub-leading contributions to the non-invertible 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).

Related papers

• Hilbert space geometry and quantum chaos [39.58317527488534]
  We consider the symmetric part of the QGT for various multi-parametric random matrix Hamiltonians. We find for a two-dimensional parameter space that, while the ergodic phase corresponds to the smooth manifold, the integrable limit marks itself as a singular geometry with a conical defect.
  arXiv  Detail & Related papers  (2024-11-18T19:00:17Z)
• Entanglement asymmetry in CFT with boundary symmetry breaking [0.0]
  We study the asymmetry of a subsystem $A$ originating from the symmetry-breaking extending into a semi-infinite bulk boundary. By employing the twist field formalism, we derive a universal expression for the asymmetry. Our exact analytical findings are validated through numerical simulations in the critical Ising and 3-state Potts models.
  arXiv  Detail & Related papers  (2024-11-15T14:56:03Z)
• Entanglement asymmetry in conformal field theory and holography [0.0]
  Entanglement asymmetry is a measure of symmetry breaking in quantum subsystems. We study the asymmetry of a class of excited "coherent states" in conformal quantum field theories with a U(1) symmetry.
  arXiv  Detail & Related papers  (2024-07-10T18:08:27Z)
• Non-invertible and higher-form symmetries in 2+1d lattice gauge theories [0.0]
  We explore exact generalized symmetries in the standard 2+1d lattice $mathbbZ$ gauge theory coupled to the Ising model. One model has a (non-anomalous) non-invertible symmetry, and we identify two distinct non-invertible symmetry protected topological phases. We discuss how the symmetries and anomalies in these two models are related by gauging, which is a 2+1d version of the Kennedy-Tasaki transformation.
  arXiv  Detail & Related papers  (2024-05-21T18:00:00Z)
• Three perspectives on entropy dynamics in a non-Hermitian two-state system [41.94295877935867]
  entropy dynamics as an indicator of physical behavior in an open two-state system with balanced gain and loss is presented. We distinguish the perspective taken in utilizing the conventional framework of Hermitian-adjoint states from an approach that is based on biorthogonal-adjoint states and a third case based on an isospectral mapping.
  arXiv  Detail & Related papers  (2024-04-04T14:45:28Z)
• Symmetry-resolved Entanglement Entropy, Spectra & Boundary Conformal Field Theory [0.0]
  We perform a comprehensive analysis of the symmetry-resolved entanglement entropy (EE) for one single interval in the ground state of a $1+1$D conformal field theory (CFT) We utilize the boundary CFT approach to study the total EE, which enables us to find the universal leading order behavior of the SREE. We derive the symmetry-resolved entanglement spectra for a CFT invariant under a finite symmetry group.
  arXiv  Detail & Related papers  (2023-09-06T18:03:14Z)
• Simultaneous Transport Evolution for Minimax Equilibria on Measures [48.82838283786807]
  Min-max optimization problems arise in several key machine learning setups, including adversarial learning and generative modeling. In this work we focus instead in finding mixed equilibria, and consider the associated lifted problem in the space of probability measures. By adding entropic regularization, our main result establishes global convergence towards the global equilibrium.
  arXiv  Detail & Related papers  (2022-02-14T02:23:16Z)
• Topological transitions with continuously monitored free fermions [68.8204255655161]
  We show the presence of a topological phase transition that is of a different universality class than that observed in stroboscopic projective circuits. We find that this entanglement transition is well identified by a combination of the bipartite entanglement entropy and the topological entanglement entropy.
  arXiv  Detail & Related papers  (2021-12-17T22:01:54Z)
• Non-Hermitian $C_{NH} = 2$ Chern insulator protected by generalized rotational symmetry [85.36456486475119]
  A non-Hermitian system is protected by the generalized rotational symmetry $H+=UHU+$ of the system. Our finding paves the way towards novel non-Hermitian topological systems characterized by large values of topological invariants.
  arXiv  Detail & Related papers  (2021-11-24T15:50:22Z)
• Entanglement Entropy of Non-Hermitian Free Fermions [59.54862183456067]
  We study the entanglement properties of non-Hermitian free fermionic models with translation symmetry. Our results show that the entanglement entropy has a logarithmic correction to the area law in both one-dimensional and two-dimensional systems.
  arXiv  Detail & Related papers  (2021-05-20T14:46:09Z)
• Boundary effects on symmetry resolved entanglement [0.0]
  We study the symmetry resolved entanglement entropies in one-dimensional systems with boundaries. We derive exact formulas for the charged and symmetry resolved entropies based on theorems and conjectures.
  arXiv  Detail & Related papers  (2020-09-17T19:34:34Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.