Volume Law and Quantum Criticality in the Entanglement Entropy of Excited Eigenstates of the Quantum Ising Model

Abstract

Much has been learned about universal properties of entanglement entropies in ground states of quantum many-body lattice systems. Here we unveil universal properties of the average bipartite entanglement entropy of eigenstates of the paradigmatic quantum Ising model in one dimension. The leading term exhibits a volume-law scaling that we argue is universal for translationally invariant quadratic models. The subleading term is constant at the critical field for the quantum phase transition and vanishes otherwise (in the thermodynamic limit), i.e., the critical field can be identified from subleading corrections to the average (over all eigenstates) entanglement entropy.

arXiv comment6+1 pages, 5 figures, as published

References in corpus (43)

• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Entanglement Entropy and Quantum Field Theory
• Area laws for the entanglement entropy - a review
• Entanglement in quantum critical phenomena
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Scaling of Entanglement close to a Quantum Phase Transitions
• Entropy and Area
• Geometric and Renormalized Entropy in Conformal Field Theory
• Entanglement entropy and conformal field theory
• Entanglement in a simple quantum phase transition
• One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
• Calculation of reduced density matrices from correlation functions
• An Area Law for One Dimensional Quantum Systems
• Reduced density matrices and entanglement entropy in free lattice models
• Generalized Gibbs ensemble in integrable lattice models
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture
• Violation of the entropic area law for Fermions
• Entanglement Properties of the Harmonic Chain
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Entanglement in XY Spin Chain
• Entanglement entropy in fermionic Laughlin states
• Entanglement scaling in critical two-dimensional fermionic and bosonic systems
• Eigenstate thermalization hypothesis (ETH) and integrability in quantum spin chains
• Entanglement entropy of excited states
• On the entanglement entropy for a XY spin chain
• Entanglement Entropy of Eigenstates of Quadratic Fermionic Hamiltonians
• Anomalies in the Entanglement Properties of the Square Lattice Heisenberg Model
• Scaling Behavior of Entanglement in Two- and Three-Dimensional Free Fermions
• Global characteristics of all eigenstates of local many-body Hamiltonians: participation ratio and entanglement entropy
• Quantum Entanglement of the Sachdev-Ye-Kitaev Models
• Statistics dependence of the entanglement entropy
• Entanglement Entropy Scaling Laws and Eigenstate Typicality in Free Fermion Systems
• Exact time-correlation functions of quantum Ising chain in a kicking transversal magnetic field
• Ellipses of Constant Entropy in the XY Spin Chain
• Entanglement in ground and excited states of gapped fermion systems and their relationship with fermi surface and thermodynamic equilibrium properties
• Bound states and entanglement in the excited states of quantum spin chains
• Eigenstate Gibbs Ensemble in Integrable Quantum Systems
• Subarea law of entanglement in nodal fermionic systems
• Information measures for a local quantum phase transition: Lattice fermions in a one-dimensional harmonic trap
• Generalized eigenstate typicality in translation-invariant quasifree fermionic models

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• Quantum magnonics: when magnon spintronics meets quantum information science
• Entanglement and matrix elements of observables in interacting integrable systems
• Geometry of variational methods: dynamics of closed quantum systems
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• The Page Curve for Fermionic Gaussian States
• Typical entanglement entropy in the presence of a center: Page curve and its variance
• Average eigenstate entanglement entropy of the XY chain in a transverse field and its universality for translationally invariant quadratic fermionic models
• Symmetry-resolved Page curves
• Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles
• Entanglement in many-body eigenstates of quantum-chaotic quadratic Hamiltonians
• Generalized Deep Thermalization for Free Fermions
• Bipartite entanglement entropy of the excited states of the free fermions and the harmonic oscillators
• Entanglement and Complexity of Purification in (1+1)-dimensional free Conformal Field Theories
• Characterizing complexity of many-body quantum dynamics by higher-order eigenstate thermalization
• Many-body dynamics in long-range hopping model in the presence of correlated and uncorrelated disorder
• Eigenstate entanglement: Crossover from the ground state to volume laws
• Entanglement and relative entropies for low-lying excited states in inhomogeneous one-dimensional quantum systems
• Quantum criticality and universality in the $p$-wave paired Aubry-André-Harper model
• Eigenstate capacity and Page curve in fermionic Gaussian states
• Entanglement production in the dynamical Casimir effect at parametric resonance
• Eigenstate entanglement entropy in $PT$ invariant non-Hermitian system
• Average entanglement entropy of midspectrum eigenstates of quantum-chaotic interacting Hamiltonians
• Minimal energy cost of entanglement extraction
• Entanglement entropy of Bell-network states in LQG: Analytical and numerical results
• Corrections to universal Rényi entropy in quasiparticle excited states of quantum chains
• Guide to Exact Diagonalization Study of Quantum Thermalization
• Entanglement of magnon excitations in spin chains
• Exponential shortcut to measurement-induced entanglement phase transitions
• Entanglement and thermodynamic entropy in a clean many-body-localized system
• Eigenstate entanglement scaling for critical interacting spin chains
• Universal Rényi Entropy of Quasiparticle Excitations
• Local optimization on pure Gaussian state manifolds
• Correlation-induced coherence and its use in detecting quantum phase transitions
• Tight-binding billiards
• Average pure-state entanglement entropy in spin systems with SU(2) symmetry
• Entanglement dualities in supersymmetry
• Observational entropic study of Anderson localization
• Bosonic and fermionic Gaussian states from Kähler structures
• Eigenstate Correlations in Dual-Unitary Quantum Circuits: Partial Spectral Form Factor
• Typical entanglement entropy in systems with particle-number conservation
• Non-Abelian entanglement asymmetry in random states
• Scaling functions for eigenstate entanglement crossovers in harmonic lattices
• Probing Hilbert space fragmentation and the block inverse participation ratio
• Eigenstate entanglement entropy in the integrable spin-$\frac{1}{2}$ XYZ model
• Nonlocal fermions and the entropy volume law
• Measurement-induced phase transition in periodically driven free-fermionic systems
• Entanglement dynamics of multi-parametric random states: a single parametric formulation
• Diagonal entropy in many-body systems: Volume effect and quantum phase transitions
• No eigenstate of the critical transverse-field Ising chain satisfies the area law
• Entanglement Clustering for ground-stateable quantum many-body states
• Average mutual information for random fermionic Gaussian quantum states
• Volume-law entanglement fragmentation of quasiparticles
• Efficient computation of average subsystem Bures distance between fermionic Gaussian states
• Localization transitions in quadratic systems without quantum chaos
• Coexistence of different scaling laws for the entanglement entropy in a periodically driven system
• Volume-law entanglement entropy of typical pure quantum states