Anomalous low-frequency conductivity in easy-plane XXZ spin chains

Abstract

In the easy-plane regime of XXZ spin chains, spin transport is ballistic, with a Drude weight that has a discontinuous fractal dependence on the value of the anisotropy $\Delta =\cos \pi \lambda$ at nonzero temperatures. We show that this structure necessarily implies the divergence of the low-frequency conductivity for generic irrational values of $\lambda$. Within the framework of generalized hydrodynamics, we show that in the high-temperature limit the low-frequency conductivity at a generic anisotropy scales as $\sigma (\omega )\sim 1/\sqrt{\omega }$; anomalous response occurs because quasiparticles undergo Lévy flights. For rational values of $\lambda$, the divergence is cut off at low frequencies and the corrections to ballistic spin transport are diffusive. We also use our approach to recover that at the isotropic point $\Delta =1$, spin transport is superdiffusive with $\sigma (\omega )\sim {\omega }^{-1/3}$. We support our results with extensive numerical studies using matrix-product operator methods.

arXiv comment5pp, 2 figs, plus supplemental material

References in corpus (87)

• The density-matrix renormalization group in the age of matrix product states
• Efficient classical simulation of slightly entangled quantum computations
• 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
• Time-dependence of correlation functions following a quantum quench
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Relaxation and Pre-thermalization in an Isolated Quantum System
• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Generalized Gibbs ensemble in integrable lattice models
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• Emergent hydrodynamics in integrable quantum systems out of equilibrium
• Time evolution of local observables after quenching to an integrable model
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Complete Generalized Gibbs Ensemble in an interacting Theory
• Entanglement and thermodynamics after a quantum quench in integrable 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
• Spin transport in a one-dimensional anisotropic Heisenberg model
• Hydrodynamic Diffusion in Integrable Systems
• Quasilocal charges in integrable lattice systems
• Spin diffusion from an inhomogeneous quench in an integrable system
• Finite temperature Drude weight of the one dimensional spin 1/2 Heisenberg model}
• Expansion dynamics of interacting bosons in homogeneous lattices in one and two dimensions
• Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems
• Bethe-Boltzmann Hydrodynamics and Spin Transport in the XXZ Chain
• Soliton gases and generalized hydrodynamics
• Constructing the generalized Gibbs ensemble after a quantum quench
• "Light-cone" dynamics after quantum quenches in spin chains
• Diffusion and ballistic transport in one-dimensional quantum systems
• Families of quasi-local conservation laws and quantum spin transport
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• Solvable Hydrodynamics of Quantum Integrable Systems
• Thermalization near integrability in a dipolar quantum Newton's cradle
• Kinetic theory of spin diffusion and superdiffusion in XXZ spin chains
• Nonequilibrium quantum dynamics and transport: from integrability to many-body localization
• Diffusion in generalized hydrodynamics and quasiparticle scattering
• Observation of universal dynamics in an isolated one-dimensional Bose gas far from equilibrium
• Large-scale description of interacting one-dimensional Bose gases: generalized hydrodynamics supersedes conventional hydrodynamics
• Microscopic origin of ideal conductivity in integrable quantum models
• Finite temperature dynamical DMRG and the Drude weight of spin-1/2 chains
• Relaxation after quantum quenches in the spin-1/2 Heisenberg XXZ chain
• Ballistic transport in the one-dimensional Hubbard model: the hydrodynamic approach
• Analytic solution of the Domain Wall non-equilibrium stationary state
• Super-diffusion in one-dimensional quantum lattice models
• A note on generalized hydrodynamics: inhomogeneous fields and other concepts
• Spin dynamics and transport in gapped one-dimensional Heisenberg antiferromagnets at nonzero temperatures
• Dynamics of hard rods with initial domain wall state
• Drude Weight for the Lieb-Liniger Bose Gas
• Prethermalization and Thermalization in Isolated Quantum Systems
• Generalized hydrodynamics with space-time inhomogeneous interactions
• Stationary behaviour of observables after a quantum quench in the spin-1/2 Heisenberg XXZ chain
• Quasilocal conservation laws in XXZ spin-1/2 chains: open, periodic and twisted boundary conditions
• Low temperature spin diffusion in the one-dimensional quantum $O(3)$ nonlinear $\sigma$-model
• Ballistic spin transport in a periodically driven integrable quantum system
• Anomalous spin diffusion in one-dimensional antiferromagnets
• Universal spin dynamics in infinite-temperature one-dimensional quantum magnets
• Operator growth and eigenstate entanglement in an interacting integrable Floquet system
• The thermodynamic limit of the Whitham equations
• Generalized Gibbs Ensemble for Heisenberg Spin Chains
• Dynamical Quasicondensation of Hard-Core Bosons at Finite Momenta
• Exactly conserved quasilocal operators for the XXZ spin chain
• Universal relaxational dynamics of gapped one dimensional models in the quantum sine-Gordon universality class
• On Generalized Gibbs Ensembles with an infinite set of conserved charges
• Transport in the sine-Gordon field theory: from generalized hydrodynamics to semiclassics
• Spin transport in the XXZ chain at finite temperature and momentum
• Anomalous relaxation and the high-temperature structure factor of XXZ spin chains
• Lower Bounding Diffusion Constant by the Curvature of Drude Weight
• Density dynamics in translationally invariant spin-1/2 chains at high temperatures: a current auto-correlation approach to finite time- and length-scales
• Non-Equilibrium Mass Transport in the 1D Fermi-Hubbard Model
• Real-time broadening of non-equilibrium density profiles and the role of the specific initial-state realization
• Transport properties of the one-dimensional Hubbard model at finite temperature
• The spin Drude weight of the XXZ chain and generalized hydrodynamics
• Spin and thermal conductivity of quantum spin ladders
• Drude weight in systems with open boundary conditions
• Heat transport of cuprate-based low-dimensional quantum magnets with strong exchange coupling
• High-temperature spin dynamics in the Heisenberg chain: Magnon propagation and emerging KPZ-scaling in the zero-magnetization limit
• Proposal for measuring the finite-temperature Drude weight of integrable systems
• Generalized hydrodynamics, quasiparticle diffusion, and anomalous local relaxation in random integrable spin chains
• Spin and energy correlations in the one dimensional spin 1/2 Heisenberg model
• A TBA description of thermal transport in the XXZ Heisenberg model
• Spin hydrodynamics in the S = 1/2 anisotropic Heisenberg chain
• Anomalous and regular transport in spin 1/2 chains: AC conductivity
• Absence of high-temperature ballistic transport in the spin-$1/2$ $XXX$ chain within the grand-canonical ensemble
• Energy-dependent 3-body loss in 1D Bose gases
• Hydrodynamics of massless integrable RG flows and a non-equilibrium c-theorem
• Finite-size anomalies of the Drude weight: role of symmetries and ensembles

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