Integrability-protected adiabatic reversibility in quantum spin chains

Abstract

We consider the out-of-equilibrium dynamics of the Heisenberg anisotropic quantum spin--$1/2$ chain threaded by a time-dependent magnetic flux. In the spirit of the recently developed generalized hydrodynamics (GHD), we exploit the integrability of the model for any flux values to derive an exact description of the dynamics in the limit of slowly varying flux: the state of the system is described at any time by a time-dependent generalized Gibbs ensemble. Two dynamical regimes emerge according to the value of the anisotropy $\Delta$. For $|\Delta |>1$, reversibility is preserved: the initial state is always recovered whenever the flux is brought back to zero. On the contrary, for $|\Delta |<1$, instabilities of quasiparticles produce irreversible dynamics as confirmed by the dramatic growth of entanglement entropy. In this regime, the standard GHD description becomes incomplete and we complement it via a maximum entropy production principle. We test our predictions against numerical simulations finding excellent agreement.

6+13 pages; 4+3 figures

References in corpus (27)

• The density-matrix renormalization group in the age of matrix product states
• Thermalization and its mechanism for generic isolated quantum systems
• Quantum Quench in the Transverse Field Ising Chain
• Experimental Observation of a Generalized Gibbs Ensemble
• Breakdown of thermalization in finite one-dimensional systems
• 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
• Hydrodynamic Diffusion in Integrable Systems
• Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems
• "Light-cone" dynamics after quantum quenches in spin chains
• Ballistic transport in the one-dimensional Hubbard model: the hydrodynamic approach
• Transport in out-of-equilibrium XXZ chains: non-ballistic behavior and correlation functions
• Dynamical Correlations after a Quantum Quench
• Generalized Gibbs Ensembles for Quantum Field Theories
• Higher-Order Hydrodynamics in 1D: a Promising Direction and a Null Result
• Entanglement evolution and generalised hydrodynamics: noninteracting systems
• 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
• Stationary states in a free fermionic chain from the Quench Action Method
• Energy transport in an integrable parafermionic chain via generalized hydrodynamics
• Breakdown of the generalized Gibbs ensemble for current-generating quenches
• Quantum quenches and Generalized Gibbs Ensemble in a Bethe Ansatz solvable lattice model of interacting bosons
• Towards a Generalized Hydrodynamics description of Rényi entropies in integrable systems
• Quasi locality of the GGE in interacting-to-free quenches in relativistic field theories
• Quasilocal charges and progress towards the complete GGE for field theories with non-diagonal scattering
• Superluminal moving defects in the Ising spin chain
• Lack of thermalization for integrability-breaking impurities

Cited by in corpus (33)

• Finite-temperature transport in one-dimensional quantum lattice models
• Diffusion in generalized hydrodynamics and quasiparticle scattering
• Lecture notes on Generalised Hydrodynamics
• Generalized hydrodynamics with space-time inhomogeneous interactions
• Anomalous spin diffusion in one-dimensional antiferromagnets
• Hydrodynamics of weak integrability breaking
• Thermalisation of a trapped one-dimensional Bose gas via diffusion
• The effect of atom losses on the distribution of rapidities in the one-dimensional Bose gas
• Generalised hydrodynamics with dephasing noise
• Domain-wall melting in the spin-$1/2$ XXZ spin chain: emergent Luttinger liquid with fractal quasi-particle charge
• Ballistic macroscopic fluctuation theory
• Generalized hydrodynamics of the KdV soliton gas
• Generalized hydrodynamics regime from the thermodynamic bootstrap program
• Generalized hydrodynamics: a perspective
• Generalized Hydrodynamics of the attractive Non-Linear Schroedinger Equation
• Exact Thermodynamics and Transport in the Classical Sine-Gordon Model
• Ballistic transport and boundary resistances in inhomogeneous quantum spin chains
• Euler-scale dynamical correlations in integrable systems with fluid motion
• Adiabatic formation of bound states in the 1d Bose gas
• The sine-Gordon model from coupled condensates: a Generalized Hydrodynamics viewpoint
• Euler-scale dynamical fluctuations in non-equilibrium interacting integrable systems
• How generalized hydrodynamics time evolution arises from a form factor expansion
• Molecular dynamics simulation of entanglement spreading in generalized hydrodynamics
• Hydrodynamics of massless integrable RG flows and a non-equilibrium c-theorem
• Hydrodynamic relaxation of spin helices
• On the Hydrodynamics of Unstable Excitations
• The Staircase Model: Massless Flows and Hydrodynamics
• Bloch oscillations in the spin-1/2 XXZ chain
• Hamiltonian formulation and aspects of integrability of generalised hydrodynamics
• Simulating generalised fluids via interacting wave packets evolution
• A hydrodynamic approach to Stark localization
• Long-lived non-thermal states in pumped one-dimensional systems of hard-core bosons
• Hydrodynamic non-linear response of interacting integrable systems