Non-abelian symmetry-resolved entanglement entropy

Abstract

We introduce a mathematical framework for symmetry-resolved entanglement entropy with a non-abelian symmetry group. To obtain a reduced density matrix that is block-diagonal in the non-abelian charges, we define subsystems operationally in terms of subalgebras of invariant observables. We derive exact formulas for the average and the variance of the typical entanglement entropy for the ensemble of random pure states with fixed non-abelian charges. We focus on compact, semisimple Lie groups. We show that, compared to the abelian case, new phenomena arise from the interplay of locality and non-abelian symmetry, such as the asymmetry of the entanglement entropy under subsystem exchange, which we show in detail by computing the Page curve of a many-body system with SU(2) symmetry.

55 pages, 5 figures; published version

References in corpus (86)

• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• Entropy and Area
• Geometric and Renormalized Entropy in Conformal Field Theory
• Average Entropy of a Subsystem
• Information in Black Hole Radiation
• Reference frames, superselection rules, and quantum information
• Notes on Some Entanglement Properties of Quantum Field Theory
• Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
• Quantum tensor product structures are observable-induced
• Remarks on entanglement entropy for gauge fields
• A Short Review of Loop Quantum Gravity
• Quantum mechanics and the covariance of physical laws in quantum reference frames
• Symmetry-resolved entanglement in many-body systems
• Decomposition of entanglement entropy in lattice gauge theory
• Polyhedra in loop quantum gravity
• The Black Hole information problem: past, present, and future
• Equipartition of the Entanglement Entropy
• White Holes as Remnants: A Surprising Scenario for the End of a Black Hole
• Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians
• Entanglement asymmetry as a probe of symmetry breaking
• Holographic Charged Renyi Entropies
• Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges
• Symmetry resolved entanglement in free fermionic systems
• A change of perspective: switching quantum reference frames via a perspective-neutral framework
• Spin-resolved entanglement spectroscopy of critical spin chains and Luttinger liquids
• Entanglement, Particle Identity and the GNS Construction: A Unifying Approach
• Entanglement and Particle Identity: A Unifying Approach
• Rényi generalization of the operational entanglement entropy
• From tunnels to towers: quantum scars from Lie Algebras and q-deformed Lie Algebras
• Entanglement constrained by superselection rules
• Dynamics of Charge-Resolved Entanglement after a Local Quench
• Dynamical entanglement entropy with angular momentum and U(1) charge
• Symmetry-resolved dynamical purification in synthetic quantum matter
• Operationally accessible entanglement of one dimensional spinless fermions
• Particle Number Fluctuations, Rényi and Symmetry-resolved Entanglement Entropy in Two-dimensional Fermi Gas from Multi-dimensional Bosonization
• Criticality and entanglement in random quantum systems
• Symmetry resolved entanglement in gapped integrable systems: a corner transfer matrix approach
• Entanglement entropy and superselection sectors I. Global symmetries
• Symmetry resolved entanglement: Exact results in 1D and beyond
• Entanglement measures and their properties in quantum field theory
• Symmetry decomposition of negativity of massless free fermions
• Algebraic Approach to Entanglement and Entropy
• Structure of chaotic eigenstates and their entanglement entropy
• Notes on the type classification of von Neumann algebras
• Symmetry-resolved entanglement in symmetry-protected topological phases
• Symmetry resolved entanglement in two-dimensional systems via dimensional reduction
• Entanglement barrier and its symmetry resolution: theory and experiment
• Symmetry-Resolved Entanglement in AdS${}_3$/CFT${}_2$ coupled to $U(1)$ Chern-Simons Theory
• Finite-size corrections in critical symmetry-resolved entanglement
• Discreteness of the volume of space from Bohr-Sommerfeld quantization
• Typical entanglement entropy in the presence of a center: Page curve and its variance
• Entanglement entropy of squeezed vacua on a lattice
• Operational Entanglement of Symmetry-Protected Topological Edge States
• Symmetry decomposition of relative entropies in conformal field theory
• Symmetry-resolved Page curves
• Non-Abelian eigenstate thermalization hypothesis
• Noncommuting conserved quantities in quantum many-body thermalization
• Gluing polyhedra with entanglement in loop quantum gravity
• Noncommuting conserved charges in quantum thermodynamics and beyond
• Non-Abelian symmetry can increase entanglement entropy
• Symmetry Resolved Entanglement of Excited States in Quantum Field Theory I: Free Theories, Twist Fields and Qubits
• Equipartition of Entanglement in Quantum Hall States
• Symmetry-resolved Entanglement Entropy, Spectra & Boundary Conformal Field Theory
• Entanglement entropy production in gravitational collapse: covariant regularization and solvable models
• Average entanglement entropy of midspectrum eigenstates of quantum-chaotic interacting Hamiltonians
• Symmetry Resolved Entanglement of Excited States in Quantum Field Theory II: Numerics, Interacting Theories and Higher Dimensions
• Entanglement entropy of Bell-network states in LQG: Analytical and numerical results
• Entropy of a subalgebra of observables and the geometric entanglement entropy
• Entanglement Entropy of ($2+1$)-Dimensional SU(2) Lattice Gauge Theory on Plaquette Chains
• Numerical Methods for Detecting Symmetries and Commutant Algebras
• Quantifying quantum chaos through microcanonical distributions of entanglement
• Symmetry-resolved modular correlation functions in free fermionic theories
• Page curve and symmetries
• Symmetry Resolved Measures in Quantum Field Theory: a Short Review
• Eigenstate thermalization hypothesis in two-dimensional XXZ model with or without SU(2) symmetry
• Average pure-state entanglement entropy in spin systems with SU(2) symmetry
• Inaccessible entanglement in symmetry protected topological phases
• Loop Quantum Gravity and Quantum Information
• Multi-charged moments and symmetry-resolved Rényi entropy of free compact boson for multiple disjoint intervals
• Eigenstate entanglement entropy in the integrable spin-$\frac{1}{2}$ XYZ model
• Symmetry Resolved Entanglement Entropy in Hyperbolic de Sitter Space
• Relative subsystems and quantum reference frame transformations
• Quantum Frame Relativity of Subsystems, Correlations and Thermodynamics
• Microcanonical Truncations of Observables in Quantum Chaotic Systems
• Channel-State duality with centers

Cited by in corpus (6)

• Symmetry breaking in chaotic many-body quantum systems at finite temperature
• Non-Abelian entanglement asymmetry in random states
• Eigenstate thermalization in spin-$\frac{1}{2}$ systems with SU(2) symmetry
• Disorder-Free Localization and Fragmentation in a Non-Abelian Lattice Gauge Theory
• Symmetry-Resolved Entanglement Entropy in Higher Dimensions
• Symmetry Properties of Quantum Dynamical Entropy