Rényi entropies after releasing the Néel state in the XXZ spin-chain

Abstract

We study the Rényi entropies in the spin-$1/2$ anisotropic Heisenberg chain after a quantum quench starting from the Néel state. The quench action method allows us to obtain the stationary Rényi entropies for arbitrary values of the index $\alpha$ as generalised free energies evaluated over a calculable thermodynamic macrostate depending on $\alpha$. We work out this macrostate for several values of $\alpha$ and of the anisotropy $\Delta$ by solving the thermodynamic Bethe ansatz equations. By varying $\alpha$ different regions of the Hamiltonian spectrum are accessed. The two extremes are $\alpha \to \infty$ for which the thermodynamic macrostate is either the ground state or a low-lying excited state (depending on $\Delta$) and $\alpha =0$ when the macrostate is the infinite temperature state. The Rényi entropies are easily obtained from the macrostate as function of $\alpha$ and a few interesting limits are analytically characterised. We provide robust numerical evidence to confirm our results using exact diagonalisation and a stochastic numerical implementation of Bethe ansatz. Finally, using tDMRG we calculate the time evolution of the Rényi entanglement entropies. For large subsystems and for any $\alpha$, their density turns out to be compatible with that of the thermodynamic Rényi entropies

38 pages, 9 figures, added acknowledgements

References in corpus (36)

• The density-matrix renormalization group in the age of matrix product states
• Thermalization and its mechanism for generic isolated quantum systems
• Real time evolution using the density matrix renormalization group
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Quantum Quench in the Transverse Field Ising Chain
• Experimental Observation of a Generalized Gibbs Ensemble
• The Luttinger model following a sudden interaction switch-on
• Exact relaxation in a class of non-equilibrium quantum lattice systems
• 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
• Validity of the GGE for quantum quenches from interacting to noninteracting models
• Generalized Gibbs Ensembles for Quantum Field Theories
• Quantum quench in the sine-Gordon model
• 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
• Quenching the XXZ spin chain: quench action approach versus generalized Gibbs ensemble
• Global characteristics of all eigenstates of local many-body Hamiltonians: participation ratio and entanglement entropy
• AdS/dCFT one-point functions of the SU(3) sector
• Entanglement dynamics in short and long-range harmonic oscillators
• Entanglement in a periodic quench
• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Entanglement spectrum degeneracy and Cardy formula in 1+1 dimensional conformal field theories
• Correlations and diagonal entropy after quantum quenches in XXZ chains
• Finite-size corrections vs. relaxation after a sudden quench
• Exact solution for the quench dynamics of a nested integrable system
• Analytical expression for a post-quench time evolution of the one-body density matrix of one-dimensional hard-core bosons
• Stationary entropies after a quench from excited states in the Ising chain
• Quasi locality of the GGE in interacting-to-free quenches in relativistic field theories
• Global large time dynamics and the generalized Gibbs ensemble
• Quasilocal charges and progress towards the complete GGE for field theories with non-diagonal scattering
• Quantum Quench in the Infinitely Repulsive Hubbard Model: the Stationary State
• Escort distribution function of work done and diagonal entropies in quenched Luttinger liquids

Cited by in corpus (51)

• Entanglement dynamics after quantum quenches in generic integrable systems
• What is an integrable quench?
• Lecture notes on Generalised Hydrodynamics
• Unitary circuits of finite depth and infinite width from quantum channels
• Sub-ballistic growth of Rényi entropies due to diffusion
• Quasiparticle dynamics of symmetry resolved entanglement after a quench: the examples of conformal field theories and free fermions
• Entanglement evolution and generalised hydrodynamics: noninteracting systems
• Exact thermalization dynamics in the "Rule 54" Quantum Cellular Automaton
• Spreading of correlations in Markovian open quantum systems
• Entanglement evolution and generalised hydrodynamics: interacting integrable systems
• Fluctuations in ballistic transport from Euler hydrodynamics
• Quantum information dynamics in multipartite integrable systems
• Quantum information scrambling after a quantum quench
• Entanglement spreading in non-equilibrium integrable systems
• Entanglement dynamics in Rule 54: Exact results and quasiparticle picture
• Entanglement revivals as a probe of scrambling in finite quantum systems
• Towards a Generalized Hydrodynamics description of Rényi entropies in integrable systems
• Spreading of entanglement and correlations after a quench with intertwined quasiparticles
• Entangled multiplets, asymmetry, and quantum Mpemba effect in dissipative systems
• Entanglement and diagonal entropies after a quench with no pair structure
• Rényi entropies of generic thermodynamic macrostates in integrable systems
• Entanglement Evolution in Lifshitz-type Scalar Theories
• Overlaps with arbitrary two-site states in the XXZ spin chain
• Signature of quantum chaos in operator entanglement in 2d CFTs
• Unbounded entanglement production via a dissipative impurity
• Integrable quenches in nested spin chains I: the exact steady states
• Hydrodynamics of quantum entropies in Ising chains with linear dissipation
• Dynamical manifestation of Gibbs paradox after a quantum quench
• Logarithmic negativity in out-of-equilibrium open free-fermion chains: An exactly solvable case
• Prethermalisation and Thermalisation in the Entanglement Dynamics
• Entanglement spreading and quasiparticle picture beyond the pair structure
• Integrable quenches in the Hubbard model
• Operator front broadening in chaotic and integrable quantum chains
• Full Counting Statistics of Charge in Quenched Quantum Gases
• On the Strong Subadditivity of the Rényi entropies for bosonic and fermionic Gaussian states
• Relaxation and entropy generation after quenching quantum spin chains
• Correlation and entanglement spreading in nested spin chains
• Post-Quantum Quench Growth of Renyi Entropies in Low Dimensional Continuum Bosonic Systems
• Entanglement dynamics of thermofield double states in integrable models
• Generalized-Hydrodynamic approach to Inhomogeneous Quenches: Correlations, Entanglement and Quantum Effects
• Entanglement Rényi Entropies from Ballistic Fluctuation Theory: the free fermionic case
• Quasi-particle spectrum and entanglement generation after a quench in the quantum Potts spin chain
• The propagator of the finite XXZ spin-$\frac{1}{2}$ chain
• Quench dynamics of Rényi negativities and the quasiparticle picture
• Reduced fidelities for free fermions out of equilibrium: From dynamical quantum phase transitions to Mpemba effect
• 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
• Entanglement of Stationary States in the Presence of Unstable Quasiparticles
• Thermodynamic symmetry resolved entanglement entropies in integrable systems
• Dynamics of charge-imbalance-resolved entanglement negativity after a quench in a free-fermion model