Rényi entropies of generic thermodynamic macrostates in integrable systems

Abstract

We study the behaviour of Rényi entropies in a generic thermodynamic macrostate of an integrable model. In the standard quench action approach to quench dynamics, the Rényi entropies may be derived from the overlaps of the initial state with Bethe eigenstates. These overlaps fix the driving term in the thermodynamic Bethe ansatz (TBA) formalism. We show that this driving term can be also reconstructed starting from the macrostate's particle densities. We then compute explicitly the stationary Rényi entropies after the quench from the dimer and the tilted Néel state in XXZ spin chains. For the former state we employ the overlap TBA approach, while for the latter we reconstruct the driving terms from the macrostate. We discuss in full details the limits that can be analytically handled and we use numerical simulations to check our results against the large time limit of the entanglement entropies.

arXiv comment22 pages, 6 figures. Figure 2 corrected, few modifications, as published

References in corpus (116)

• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
• Real time evolution using the density matrix renormalization group
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Time-dependence of correlation functions following a quantum quench
• Measuring entanglement entropy through the interference of quantum many-body twins
• Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
• Quantum thermalization through entanglement in an isolated many-body system
• Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
• Operator Spreading in Random Unitary Circuits
• Quantum Quench in the Transverse Field Ising Chain
• Generalized Gibbs ensemble in integrable lattice models
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Experimental Observation of a Generalized Gibbs Ensemble
• Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
• Time evolution of local observables after quenching to an integrable model
• Ballistic spreading of entanglement in a diffusive nonintegrable system
• The Luttinger model following a sudden interaction switch-on
• Complete Generalized Gibbs Ensemble in an interacting Theory
• Entanglement and thermodynamics after a quantum quench in integrable systems
• Exact relaxation in a class of non-equilibrium quantum lattice systems
• Entropy scaling and simulability by Matrix Product States
• Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• Entanglement spectrum in one-dimensional systems
• Dephasing and the steady state in quantum many-particle systems
• Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
• Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
• Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
• Real time confinement following a quantum quench to a non-integrable model
• Alternatives to Eigenstate Thermalization
• Reduced Density Matrix after a Quantum Quench
• Can One Trust Quantum Simulators?
• Solution for an interaction quench in the Lieb-Liniger Bose gas
• Entanglement dynamics after quantum quenches in generic integrable systems
• Rényi Entropies from Random Quenches in Atomic Hubbard and Spin Models
• "Light-cone" dynamics after quantum quenches in spin chains
• Conformal Field Theory for Inhomogeneous One-dimensional Quantum Systems: the Example of Non-Interacting Fermi Gases
• Quantum Quenches in Integrable Field Theories
• What is an integrable quench?
• Relaxation after quantum quenches in the spin-1/2 Heisenberg XXZ chain
• Microscopic diagonal entropy and its connection to basic thermodynamic relations
• A quantum central limit theorem for non-equilibrium systems: Exact local relaxation of correlated states
• Validity of the GGE for quantum quenches from interacting to noninteracting models
• Analytic results for a quantum quench from free to hard-core one dimensional bosons
• Generalized Gibbs Ensembles for Quantum Field Theories
• Entanglement growth and correlation spreading with variable-range interactions in spin and fermionic tunnelling models
• Equilibration of a Tonks-Girardeau gas following a trap release
• Entropy of isolated quantum systems after a quench
• One-point Functions in Defect CFT and Integrability
• On the definition of a unique effective temperature for non-equilibrium critical systems
• Thermalization and Quantum Correlations in Exactly Solvable Models
• Quantum quench in the sine-Gordon model
• Entanglement scaling of operators: a conformal field theory approach, with a glimpse of simulability of long-time dynamics in 1+1d
• The microscopic origin of thermodynamic entropy in isolated systems
• Stationary behaviour of observables after a quantum quench in the spin-1/2 Heisenberg XXZ chain
• Entanglement Entropy and Twist Fields
• Generalized TBA and generalized Gibbs
• The KPZ equation with flat initial condition and the directed polymer with one free end
• Dynamics of entanglement and transport in 1D systems with quenched randomness
• One-point Functions in AdS/dCFT from Matrix Product States
• Quantum Quenches in the Thermodynamic Limit
• Multi-particle bound state formation following a quantum quench to the one-dimensional Bose gas with attractive interactions
• On entropy growth and the hardness of simulating time evolution
• Quenching the XXZ spin chain: quench action approach versus generalized Gibbs ensemble
• Quantum quenches from integrability: the fermionic pairing model
• Quench dynamics of a Tonks-Girardeau gas released from a harmonic trap
• Quench action and Renyi entropies in integrable systems
• AdS/dCFT one-point functions of the SU(3) sector
• Global characteristics of all eigenstates of local many-body Hamiltonians: participation ratio and entanglement entropy
• Universality in volume law entanglement of pure quantum states
• Exact steady states for quantum quenches in integrable Heisenberg spin chains
• Entanglement Growth after a Global Quench in Free Scalar Field Theory
• Weak and strong typicality in quantum systems
• Entanglement dynamics in short and long-range harmonic oscillators
• Multi-speed prethermalization in spin models with power-law decaying interactions
• Zamolodchikov-Faddeev Algebra and Quantum Quenches in Integrable Field Theories
• Quantum quenches in the sinh-Gordon model: steady state and one point correlation functions
• Hybrid semiclassical theory of quantum quenches in one dimensional systems
• Entanglement in a periodic quench
• On Generalized Gibbs Ensembles with an infinite set of conserved charges
• Quantum quenches from excited states in the Ising chain
• Linear growth of the entanglement entropy and the Kolmogorov-Sinai rate
• Entanglement spectrum degeneracy and Cardy formula in 1+1 dimensional conformal field theories
• Fundamental Asymmetry in Quenches Between Integrable and Nonintegrable Systems
• Initial states in integrable quantum field theory quenches from an integral equation hierarchy
• Correlations and diagonal entropy after quantum quenches in XXZ chains
• Bethe Ansatz approach to quench dynamics in the Richardson model
• Overlaps after quantum quenches in the sine-Gordon model
• Finite-size corrections vs. relaxation after a sudden quench
• Quantum quench within the gapless phase of the spin-1/2 Heisenberg XXZ spin-chain
• Entanglement production in bosonic systems: Linear and logarithmic growth
• Quantum quenches to the attractive one-dimensional Bose gas: exact results
• Rényi entropies after releasing the Néel state in the XXZ spin-chain
• Memory-preserving equilibration after a quantum quench in a 1d critical model
• Exact solution for the quench dynamics of a nested integrable system
• Exact methods in analysis of nonequilibrium dynamics of integrable models: application to the study of correlation functions in nonequilibrium 1D Bose gas
• Front dynamics and entanglement in the XXZ chain with a gradient
• Overlaps of Partial Neel States and Bethe States
• Entanglement growth and simulation efficiency in one-dimensional quantum lattice systems
• Stationary entropies after a quench from excited states in the Ising chain
• Recursive formulas for the overlaps between Bethe states and product states in XXZ Heisenberg chains
• Quasi locality of the GGE in interacting-to-free quenches in relativistic field theories
• The quench action approach in finite integrable spin chains
• Global large time dynamics and the generalized Gibbs ensemble
• Overlap distributions for quantum quenches in the anisotropic Heisenberg chain
• Quasilocal charges and progress towards the complete GGE for field theories with non-diagonal scattering
• Light-cone velocities after a global quench in a non-interacting model
• Entanglement Spectroscopy using Quantum Monte Carlo
• Temperature driven quenches in the Ising model: appearance of negative Rényi mutual information
• Real-time dynamics in a strongly interacting bosonic hopping model: Global quenches and mapping to the XX chain
• Quantum Quench in the Infinitely Repulsive Hubbard Model: the Stationary State

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• Generalized-Hydrodynamic approach to Inhomogeneous Quenches: Correlations, Entanglement and Quantum Effects
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• Quasi-particle spectrum and entanglement generation after a quench in the quantum Potts spin chain
• Entanglement Rényi Entropies from Ballistic Fluctuation Theory: the free fermionic case
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• Exact quench dynamics of symmetry resolved entanglement in a free fermion chain
• Entanglement dynamics of multi-parametric random states: a single parametric formulation
• Growth of Rényi Entropies in Interacting Integrable Models and the Breakdown of the Quasiparticle Picture
• Thermodynamic symmetry resolved entanglement entropies in integrable systems
• Entanglement of Stationary States in the Presence of Unstable Quasiparticles
• No eigenstate of the critical transverse-field Ising chain satisfies the area law
• Dynamics of charge-imbalance-resolved entanglement negativity after a quench in a free-fermion model