Low-Temperature Transport in Out-of-Equilibrium XXZ Chains

Abstract

We study the low-temperature transport properties of out-of-equilibrium XXZ spin-$1/2$ chains. We consider the protocol where two semi-infinite chains are prepared in two thermal states at small but different temperatures and suddenly joined together. We focus on the qualitative and quantitative features of the profiles of local observables, which at large times $t$ and distances $x$ from the junction become functions of the ratio $\zeta =x/t$. By means of the generalized hydrodynamic equations, we analyse the rich phenomenology arising by considering different regimes of the phase diagram. In the gapped phases, variations of the profiles are found to be exponentially small in the temperatures but described by non-trivial functions of $\zeta$. We provide analytical formulae for the latter, which give accurate results also for small but finite temperatures. In the gapless regime, we show how the three-step conformal predictions for the profiles of energy density and energy current are naturally recovered from the hydrodynamic equations. Moreover, we also recover the recent non-linear Luttinger liquid predictions for low-temperature transport: universal peaks of width $\Delta \zeta \propto T$ emerge at the edges of the light cone in the profiles of generic observables. Such peaks are described by the same function of $\zeta$ for all local observables.

38 pages, 8 figures; v2: minor revision

References in corpus (29)

• Many-Body Physics with Ultracold Gases
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Experimental Observation of a Generalized Gibbs Ensemble
• Spin transport in a one-dimensional anisotropic Heisenberg model
• "Light-cone" dynamics after quantum quenches in spin chains
• Ballistic transport in the one-dimensional Hubbard model: the hydrodynamic approach
• Conservation laws, integrability and transport in one-dimensional quantum systems
• Transport in out-of-equilibrium XXZ chains: non-ballistic behavior and correlation functions
• Full counting statistics in a propagating quantum front and random matrix spectra
• Entanglement negativity in the harmonic chain out of equilibrium
• From Interacting Particles to Equilibrium Statistical Ensembles
• Relaxation in the XX quantum chain
• Stationary states in a free fermionic chain from the Quench Action Method
• Energy transport in Heisenberg chains beyond the Luttinger liquid paradigm
• Correlations and diagonal entropy after quantum quenches in XXZ chains
• Density dynamics in translationally invariant spin-1/2 chains at high temperatures: a current auto-correlation approach to finite time- and length-scales
• Universal front propagation in the quantum Ising chain with domain-wall initial states
• Time evolution of 1D gapless models from a domain-wall initial state: SLE continued?
• Exact solution for the quench dynamics of a nested integrable system
• Short distance correlators in the XXZ spin chain for arbitrary string distributions
• Transport properties of the one-dimensional Hubbard model at finite temperature
• Charges and currents in quantum spin chains: late-time dynamics and spontaneous currents
• Approximate light cone effects in a non-relativistic quantum field theory after a local quench
• On Classical Integrability of the Hydrodynamics of Quantum Integrable Systems
• Luttinger Liquid in Non-equilibrium Steady State
• Decay of currents for strong interactions
• Spinon and bound state excitation "light cones" in Heisenberg XXZ Chains
• Non-equilibrium thermal transport and vacuum expansion in the Hubbard model
• Quantum adiabatic protocols using emergent local Hamiltonians

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• Domain-wall melting in the spin-$1/2$ XXZ spin chain: emergent Luttinger liquid with fractal quasi-particle charge
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• Integrability-protected adiabatic reversibility in quantum spin chains
• Locally quasi-stationary states in noninteracting spin chains
• From the sinh-Gordon field theory to the one-dimensional Bose gas: exact local correlations and full counting statistics
• Anomalous transport from hot quasiparticles in interacting spin chains
• Time-dependent matrix product ansatz for interacting reversible dynamics
• Integrable Matrix Models in Discrete Space-Time
• Generalized Hydrodynamic approach to charge and energy currents in the one-dimensional Hubbard model
• Quench action and large deviations: work statistics in the one-dimensional Bose gas
• Generalized hydrodynamics study of the one-dimensional Hubbard model: Stationary clogging and proportionality of spin, charge, and energy currents
• Real-time spin-charge separation in one-dimensional Fermi gases from generalized hydrodynamics
• Semiclassical theory of front propagation and front equilibration following an inhomogeneous quantum quench
• Quantum dynamics of impenetrable SU(N) fermions in one-dimensional lattices
• Euler-scale dynamical fluctuations in non-equilibrium interacting integrable systems
• Molecular dynamics simulation of entanglement spreading in generalized hydrodynamics
• Emergent ballistic transport of Bose-Fermi mixtures in one dimension
• Hydrodynamics of massless integrable RG flows and a non-equilibrium c-theorem
• Generalized-Hydrodynamic approach to Inhomogeneous Quenches: Correlations, Entanglement and Quantum Effects
• Connected correlations in partitioning protocols: a case study and beyond
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• Energy transport between critical one-dimensional systems with different central charges
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