Ballistic-to-diffusive transition in spin chains with broken integrability
arXiv:2006.13891 · doi:10.1103/PhysRevB.102.184304
Abstract
We study the ballistic-to-diffusive transition induced by the weak breaking of integrability in a boundary-driven XXZ spin-chain. Studying the evolution of the spin current density as a function of the system size , we show that, accounting for boundary effects, the transition has a non-trivial universal behavior close to the XX limit. It is controlled by the scattering length , where is the strength of the integrability breaking term. In the XXZ model, the interplay of interactions controls the emergence of a transient "quasi-ballistic" regime at length scales much shorter than . This parametrically large regime is characterized by a strong renormalization of the current which forbids a universal scaling, unlike the XX model. Our results are based on Matrix Product Operator numerical simulations and agree with perturbative analytical calculations.
arXiv comment13 pages, 9 figures
References in corpus (69)
- The density-matrix renormalization group
- Chaos and Quantum Thermalization
- Thermalization and its mechanism for generic isolated quantum systems
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- 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
- Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
- Relaxation and Pre-thermalization in an Isolated Quantum System
- Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
- Non-equilibrium coherence dynamics in one-dimensional Bose gases
- Quench dynamics and relaxation in isolated integrable quantum spin chains
- Emergent hydrodynamics in integrable quantum systems out of equilibrium
- Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
- Transport and conservation laws
- Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
- Third quantization: a general method to solve master equations for quadratic open Fermi systems
- Complete Generalized Gibbs Ensemble in an interacting Theory
- Quantum quenches in 1+1 dimensional conformal field theories
- Spin transport in a one-dimensional anisotropic Heisenberg model
- Hydrodynamic Diffusion in Integrable Systems
- Spin diffusion from an inhomogeneous quench in an integrable system
- A thermoelectric heat engine with ultracold atoms
- Finite temperature Drude weight of the one dimensional spin 1/2 Heisenberg model}
- Minimally entangled typical quantum states at finite temperature
- Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
- Thermalization near integrability in a dipolar quantum Newton's cradle
- Matrix product simulations of non-equilibrium steady states of quantum spin chains
- Kinetic theory of spin diffusion and superdiffusion in XXZ spin chains
- Observation of Quantized Conductance in Neutral Matter
- Microscopic origin of ideal conductivity in integrable quantum models
- Conformal field theory out of equilibrium: a review
- Anomalous thermalization in ergodic systems
- Thermal transport in a Luttinger liquid
- Super-diffusion in one-dimensional quantum lattice models
- Exact solution for a diffusive nonequilibrium steady state of an open quantum chain
- Adiabatic eigenstate deformations as a sensitive probe for quantum chaos
- Prethermalization and Thermalization in Isolated Quantum Systems
- Eigenstate Thermalization in a Locally Perturbed Integrable System
- Transport in Almost Integrable Models: Perturbed Heisenberg Chains
- Diffusive hydrodynamics from integrability breaking
- Crossover between ballistic and diffusive transport: The Quantum Exclusion Process
- Perturbative approach to Markovian open quantum systems
- Superdiffusion from emergent classical solitons in quantum spin chains
- Thermalization of Interacting Fermions and Delocalization in Fock space
- Anomalous Thermal Transport in Quantum Wires
- Band and correlated insulators of cold fermions in a mesoscopic lattice
- Kardar-Parisi-Zhang Scaling for an Integrable Lattice Landau-Lifshitz Spin Chain
- Quantum information scrambling after a quantum quench
- Low-frequency behavior of off-diagonal matrix elements in the integrable XXZ chain and in a locally perturbed quantum-chaotic XXZ chain
- Transport in a disordered tight-binding chain with dephasing
- High-temperature coherent transport in the XXZ chain in the presence of an impurity
- Stochastic dissipative quantum spin chains (I) : Quantum fluctuating discrete hydrodynamics
- Extending the range of real time density matrix renormalization group simulations
- Solutions for dissipative quadratic open systems: part II - fermions
- Solutions for dissipative quadratic open systems: part I - bosons
- Finite-temperature magnetization transport of the one-dimensional anisotropic Heisenberg model
- A matrix product solution for a nonequilibrium steady state of an XX chain
- Weak integrability breaking: chaos with integrability signature in coherent diffusion
- Asymmetry in energy versus spin transport in certain interacting, disordered systems
- Transport in quantum chains under strong monitoring
- Chaos Thresholds in finite Fermi systems
- Universal Hall Response in Synthetic Dimensions
- Superdiffusive transport of energy in one-dimensional metals
- Nonequilibrium steady-state Kubo formula: equality of transport coefficients
- Ballistic transport and boundary resistances in inhomogeneous quantum spin chains
- The quantized Hall conductance of a single atomic wire: A proposal based on synthetic dimensions
- Violation of the Wiedemann-Franz Law for ultracold atomic gases
- Anomalous and regular transport in spin 1/2 chains: AC conductivity
- Vanishing Hall Response of Charged Fermions in a Transverse Magnetic Field
- High order non-unitary split-step decomposition of unitary operators
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- Weak integrability breaking: chaos with integrability signature in coherent diffusion
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- Generic transport formula for a system driven by Markovian reservoirs
- Superdiffusive Energy Transport in Kinetically Constrained Models
- Weak integrability breaking perturbations of integrable models
- Less is more: more scattering leading to less resistance
- Integrability breaking in the Rule 54 cellular automaton
- Semi-classical theory of quantum stochastic resistors
- Efficient quantum information probes of non-equilibrium quantum criticality
- Absence of superdiffusion in the quasiperiodic spin chain at weak integrability breaking
- Thermal Drude weight in an integrable chiral clock model
- A theory of quasiballistic spin transport
- Energy transport in Z3 chiral clock model