Multiple relaxation times in perturbed XXZ chain

Abstract

We numerically study the relaxation of correlation functions in weakly perturbed integrable XXZ chain. The decay of the spin-current and the energy-current correlations at zero magnetization are well described by single, but quite distinct, relaxation rates governed by the square of the perturbation strength $g$. However, at finite magnetization a single correlation function reveals multiple relaxation rates. The result can be understood in terms of multi-scale relaxation scenario, where various relaxation times are linked with various quantities which are conserved in the reference integrable system. On the other hand, the correlations of non-commuting quantities, being conserved at particular anisotropies $\Delta$, decay non-exponentially with characteristic time scale linear in $g$.

References in corpus (41)

• 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
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Transport and conservation laws
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Complete Generalized Gibbs Ensemble in an interacting Theory
• Finite-temperature transport in one-dimensional quantum lattice models
• Generalized Thermalization in an Integrable Lattice System
• 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
• Generalized Gibbs ensemble prediction of prethermalization plateaus and their relation to nonthermal steady states in integrable systems
• Families of quasi-local conservation laws and quantum spin transport
• Prethermalization and thermalization in models with weak integrability breaking
• Super-diffusion in one-dimensional quantum lattice models
• Quench Dynamics in a Model with Tuneable Integrability Breaking
• Prethermalization and Thermalization in Isolated Quantum Systems
• Time evolution of a quantum many-body system: transition from integrability to ergodicity in thermodynamic limit
• On Conservation Laws, Relaxation and Pre-relaxation after a Quantum Quench
• Superdiffusion in spin chains
• Transport in Almost Integrable Models: Perturbed Heisenberg Chains
• Diffusive hydrodynamics from integrability breaking
• Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One Dimensional Bose Gases
• Hydrodynamics of weak integrability breaking
• Thermalization and light cones in a model with weak integrability breaking
• Failure of the GGE hypothesis for integrable models with bound states
• Finite Temperature Dynamical Correlations using the Microcanonical Ensemble and the Lanczos Algorithm
• Universality in the onset of quantum chaos in many-body systems
• Exactly conserved quasilocal operators for the XXZ spin chain
• Time-dependent generalized Gibbs ensembles in open quantum systems
• Spin conductivity in almost integrable spin chains
• High temperature thermal conductivity of 2-leg spin-1/2 ladders
• Local and Quasilocal Conserved Quantities in Integrable Systems
• Breakdown of the generalized Gibbs ensemble for current-generating quenches
• Quasilocal conservation laws from semicyclic irreducible representations of $U_q({\mathfrak{sl}}_2)$ in $XXZ$ spin-$1/2$ chains
• Quantum Quenches and Relaxation Dynamics in the Thermodynamic Limit
• Scaling of electrical and thermal conductivities in an almost integrable chain
• Anomalous low-frequency conductivity in easy-plane XXZ spin chains
• Lower bounds for the conductivities of correlated quantum systems
• Self-consistent approach to many-body localization and subdiffusion
• Coexistence of diffusive and ballistic transport in integrable quantum lattice models
• Ballistic transport in integrable quantum chains with degenerate spectra

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• Spin diffusion in perturbed isotropic Heisenberg spin chain
• From dissipationless to normal diffusion in easy-axis Heisenberg spin chain
• Long-living prethermalization in nearly integrable spin ladders
• Thouless approach in transport in integrable and perturbed easy-axis Heisenberg chains
• Hierarchy of timescales in a disordered spin-$1/2$ XX ladder
• Tunable Hilbert space fragmentation and extended critical regime