Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models

Abstract

We consider the problem of the decomposition of the Rényi entanglement entropies in theories with a non-abelian symmetry by doing a thorough analysis of Wess-Zumino-Witten (WZW) models. We first consider $SU(2{)}_k$ as a case study and then generalise to an arbitrary non-abelian Lie group. We find that at leading order in the subsystem size $L$ the entanglement is equally distributed among the different sectors labelled by the irreducible representation of the associated algebra. We also identify the leading term that breaks this equipartition: it does not depend on $L$ but only on the dimension of the representation. Moreover, a $\log \log L$ contribution to the Rényi entropies exhibits a universal form related to the underlying symmetry group of the model, i.e. the dimension of the Lie group.

31 pages, v2: minor changes

References in corpus (19)

• Towards a derivation of holographic entanglement entropy
• Entanglement spectrum in one-dimensional systems
• Entanglement hamiltonians in two-dimensional conformal field theory
• Symmetry-resolved entanglement detection using partial transpose moments
• Entanglement and symmetry resolution in two dimensional free quantum field theories
• Spin-resolved entanglement spectroscopy of critical spin chains and Luttinger liquids
• Entanglement equipartition in critical random spin chains
• Efficient Basis Formulation for (1+1)-Dimensional SU(2) Lattice Gauge Theory: Spectral calculations with matrix product states
• Symmetry-resolved dynamical purification in synthetic quantum matter
• Symmetry decomposition of negativity of massless free fermions
• Symmetry resolved relative entropies and distances in conformal field theory
• Entanglement spectrum degeneracy and Cardy formula in 1+1 dimensional conformal field theories
• Symmetry-Resolved Entanglement in AdS${}_3$/CFT${}_2$ coupled to $U(1)$ Chern-Simons Theory
• Branch Point Twist Field Form Factors in the sine-Gordon Model II: Composite Twist Fields and Symmetry Resolved Entanglement
• Symmetry decomposition of relative entropies in conformal field theory
• Lectures on entanglement entropy in field theory and holography
• Chiral SU(2)_k currents as local operators in vertex models and spin chains
• Entanglement Measures in a Nonequilibrium Steady State: Exact Results in One Dimension
• Exact quench dynamics of symmetry resolved entanglement in a free fermion chain

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• Symmetry-resolved entanglement in a long-range free-fermion chain
• Non-Abelian symmetry can increase entanglement entropy
• Symmetric inseparability and number entanglement in charge conserving mixed states
• Entanglement of the $3$-State Potts Model via Form Factor Bootstrap: Total and Symmetry Resolved Entropies
• Symmetry Resolved Entanglement of Excited States in Quantum Field Theory I: Free Theories, Twist Fields and Qubits
• Charged Rényi negativity of massless free bosons
• Entanglement resolution of free Dirac fermions on a torus
• Multi-charged moments of two intervals in conformal field theory
• Symmetry-resolved entanglement entropy in critical free-fermion chains
• Exact hydrodynamic description of symmetry-resolved Rényi entropies after a quantum quench
• Symmetry Resolved Entanglement of Excited States in Quantum Field Theory II: Numerics, Interacting Theories and Higher Dimensions
• Universal Thermal Corrections to Symmetry-Resolved Entanglement Entropy and Full Counting Statistics
• Two-Point Functions of Composite Twist Fields in the Ising Field Theory
• Entanglement asymmetry in the critical XXZ spin chain
• Page curve and symmetries
• Reduced density matrix and entanglement in interacting quantum field theory with Hamiltonian truncation
• Probing RG flows, symmetry resolution and quench dynamics through the capacity of entanglement
• Charge imbalance resolved Rényi negativity for free compact boson: Two disjoint interval case
• Dynamics of charge imbalance resolved negativity after a global quench in free scalar field theory
• Symmetry-resolved entanglement of 2D symmetry-protected topological states
• A Path Integral Ground State Monte Carlo Algorithm for Entanglement of Lattice Bosons
• The operator algebra of cyclic orbifolds
• Charge fluctuation entropy of Hawking radiation: a replica-free way to find large entropy
• On symmetry-resolved generalized entropies
• Thermodynamic symmetry resolved entanglement entropies in integrable systems
• Dynamics of charge-imbalance-resolved entanglement negativity after a quench in a free-fermion model
• Shape Deformations of Charged Rényi Entropies from Holography