Symmetry-resolved Page curves

Abstract

Given a statistical ensemble of quantum states, the corresponding Page curve quantifies the average entanglement entropy associated with each possible spatial bipartition of the system. In this work, we study a natural extension in the presence of a conservation law and introduce the symmetry-resolved Page curves, characterizing average bipartite symmetry-resolved entanglement entropies. We derive explicit analytic formulae for two important statistical ensembles with a $U(1)$-symmetry: Haar-random pure states and random fermionic Gaussian states. In the former case, the symmetry-resolved Page curves can be obtained in an elementary way from the knowledge of the standard one. This is not true for random fermionic Gaussian states. In this case, we derive an analytic result in the thermodynamic limit based on a combination of techniques from random-matrix and large-deviation theories. We test our predictions against numerical calculations and discuss the sub-leading finite-size corrections.

13 pages, 4 Figures

References in corpus (47)

• The large deviation approach to statistical mechanics
• Black holes as mirrors: quantum information in random subsystems
• Aspects of generic entanglement
• Extreme Value Statistics of Eigenvalues of Gaussian Random Matrices
• Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians
• Absence of true localization in many-body localized phases
• Quasiparticle dynamics of symmetry resolved entanglement after a quench: the examples of conformal field theories and free fermions
• Statistical distribution of quantum entanglement for a random bipartite state
• 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
• Symmetry-resolved dynamical purification in synthetic quantum matter
• Distributions of Conductance and Shot Noise and Associated Phase Transitions
• Symmetry decomposition of negativity of massless free fermions
• Entanglement spectrum of random-singlet quantum critical points
• Symmetry resolved relative entropies and distances in conformal field theory
• Symmetry resolved entanglement in integrable field theories via form factor bootstrap
• Symmetry-Resolved Entanglement in AdS${}_3$/CFT${}_2$ coupled to $U(1)$ Chern-Simons Theory
• U(1) symmetry resolved entanglement in free 1+1 dimensional field theories via form factor bootstrap
• Finite-size corrections in critical symmetry-resolved entanglement
• The Page Curve for Fermionic Gaussian States
• Symmetry-resolved entanglement for excited states and two entangling intervals in AdS${}_3$/CFT${}_2$
• Boundary effects on symmetry resolved entanglement
• Symmetry decomposition of relative entropies in conformal field theory
• Branch Point Twist Field Form Factors in the sine-Gordon Model II: Composite Twist Fields and Symmetry Resolved Entanglement
• Entanglement of random vectors
• Entanglement negativity spectrum of random mixed states: A diagrammatic approach
• Entanglement in many-body eigenstates of quantum-chaotic quadratic Hamiltonians
• Entanglement distribution in the Quantum Symmetric Simple Exclusion Process
• Charged Moments in $W_3$ Higher Spin Holography
• Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State
• Symmetry-resolved entanglement in a long-range free-fermion chain
• A Proof of Vivo-Pato-Oshanin's Conjecture on the Fluctuation of von Neumann Entropy
• Symmetric inseparability and number entanglement in charge conserving mixed states
• Charged Rényi negativity of massless free bosons
• Dynamics of Fluctuations in Quantum Simple Exclusion Processes
• Equipartition of Entanglement in Quantum Hall States
• Distribution of G-concurrence of random pure states
• Page Curve for Entanglement Negativity through Geometric Evaporation
• Theory of Non-Interacting Fermions and Bosons in the Canonical Ensemble
• Negativity Spectra in Random Tensor Networks and Holography
• Symmetry-resolved entanglement entropy in critical free-fermion chains
• Exact hydrodynamic description of symmetry-resolved Rényi entropies after a quantum quench
• Observing Floquet topological order by symmetry resolution
• Spectral Properties of the Jacobi Ensembles via the Coulomb Gas approach
• Dynamics of charge imbalance resolved negativity after a global quench in free scalar field theory
• Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models

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• Surprises in the Deep Hilbert Space of all-to-all systems: From super-exponential scrambling to slow entanglement growth
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• Symmetry Resolved Measures in Quantum Field Theory: a Short Review
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• Entanglement entropy along a massless renormalisation flow: the tricritical to critical Ising crossover
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• Average Rényi Entanglement Entropy in Gaussian Boson Sampling
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• Symmetry-resolved genuine multi-entropy: Haar random and graph states
• Additional quantum many-body scars of the spin-$1$ $XY$ model with Fock-space cages and commutant algebras
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