Logarithmic current fluctuations in non-equilibrium quantum spin chains

Abstract

We study zero-temperature quantum spin chains which are characterized by a non-vanishing current. For the XX model starting from the initial state |... + + + - - - ...> we derive an exact expression for the variance of the total spin current. We show that asymptotically the variance exhibits an anomalously slow logarithmic growth; we also extract the sub-leading constant term. We then argue that the logarithmic growth remains valid for the XXZ model in the critical region.

9 pages, 4 figures, minor alterations

References in corpus (30)

• Shot Noise in Mesoscopic Conductors
• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Shape Fluctuations and Random Matrices
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Universal Distributions for Growth Processes in 1+1 Dimensions and Random Matrices
• Quantum Noise as an Entanglement Meter
• Current fluctuations in non-equilibrium diffusive systems: an additivity principle
• Exact Large Deviation Function in the Asymmetric Exclusion Process
• Real-time dynamics in spin-1/2 chains with adaptive time-dependent DMRG
• Transport in the XX chain at zero temperature: Emergence of flat magnetization profiles
• Scaling Limit for the Space-Time Covariance of the Stationary Totally Asymmetric Simple Exclusion Process
• Spatial correlations of the 1D KPZ surface on a flat substrate
• Long range correlations in the non-equilibrium quantum relaxation of a spin chain
• Full counting statistics for noninteracting fermions: Exact results and the Levitov-Lesovik formula
• Current fluctuations in the zero-range process with open boundaries
• Exact Correlation Amplitude for the S=1/2 Heisenberg Antiferromagnetic Chain
• Dynamic scaling of fronts in the quantum XX chain
• Correlation amplitude for the XXZ spin chain in the disordered regime
• Relaxation in the XX quantum chain
• Nonequilibrium Steady State in a Quantum System: One-dimensional Transverse Ising Model with Energy Current
• Scaling and front dynamics in Ising quantum chains
• Isotropic Transverse XY Chain with Energy- and Magnetization Currents
• The Diffusion of the Magnetization Profile in the XX-model
• Magnetization distribution in the transverse Ising chain with energy flux
• Current Fluctuations in the exclusion process and Bethe Ansatz
• Lagrange multiplier based transport theory for quantum wires
• Presence of energy flux in quantum spin chains: An experimental signature
• Long-Time Tails and Anomalous Slowing Down in the Relaxation of Spatially Inhomogeneous Excitations in Quantum Spin Chains
• Lattice field theories with an energy current
• Off equilibrium dynamics in disordered quantum spin chain

Cited by in corpus (73)

• Emergent hydrodynamics in integrable quantum systems out of equilibrium
• Finite-temperature transport in one-dimensional quantum lattice models
• Quantum quenches in 1+1 dimensional conformal field theories
• Conformal Field Theory for Inhomogeneous One-dimensional Quantum Systems: the Example of Non-Interacting Fermi Gases
• Full counting statistics in a propagating quantum front and random matrix spectra
• Current fluctuations and transport efficiency for general Langevin systems
• A note on generalized hydrodynamics: inhomogeneous fields and other concepts
• Dynamics of hard rods with initial domain wall state
• Inhomogeneous field theory inside the arctic circle
• Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition
• Non-equilibrium steady states in the quantum XXZ spin chain
• Quantum dynamics with stochastic reset
• Quench dynamics of a Tonks-Girardeau gas released from a harmonic trap
• Crossover between ballistic and diffusive transport: The Quantum Exclusion Process
• Inhomogeneous quenches in a fermionic chain: exact results
• Quantum quench from a thermal tensor state: boundary effects and generalized Gibbs ensemble
• Dynamical Quasicondensation of Hard-Core Bosons at Finite Momenta
• Entanglement spreading after a geometric quench in quantum spin chains
• Dynamics of the spin-1/2 Heisenberg chain initialized in a domain-wall state
• Inhomogeneous quenches in the transverse field Ising chain: scaling and front dynamics
• On entanglement evolution across defects in critical chains
• Ballistic front dynamics after joining two semi-infinite quantum Ising chains
• Exact large-deviation statistics for a nonequilibrium quantum spin chain
• Universal front propagation in the quantum Ising chain with domain-wall initial states
• Front dynamics and entanglement in the XXZ chain with a gradient
• Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain
• Time Evolution within a Comoving Window: Scaling of signal fronts and magnetization plateaus after a local quench in quantum spin chains
• Mobility edge and multifractality in a periodically driven Aubry-André model
• Exactly solvable counting statistics in weakly coupled open interacting spin systems
• Dynamical simulation of integrable and non-integrable models in the Heisenberg picture
• Fredholm determinants, full counting statistics and Loschmidt echo for domain wall profiles in one-dimensional free fermionic chains
• Out-of-equilibrium dynamics in a quantum impurity model: numerics for particle transport and entanglement entropy
• Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point
• Hydrodynamical phase transition for domain-wall melting in the XY chain
• Non-equilibrium quantum transport in presence of a defect: the non-interacting case
• Magnetization and entanglement after a geometric quench in the XXZ chain
• Entanglement entropies of inhomogeneous Luttinger liquids
• Free fermions at the edge of interacting systems
• Exact entanglement growth of a one-dimensional hard-core quantum gas during a free expansion
• Exact hydrodynamic solution of a double domain wall melting in the spin-1/2 XXZ model
• Non-equilibrium transport in $d$-dimensional non-interacting Fermi gases
• Noninteracting fermionic systems with localized losses: Exact results in the hydrodynamic limit
• Entanglement evolution across defects in critical anisotropic Heisenberg chains
• Surface and bulk entanglement in free-fermion chains
• Free Fermions with a Localized Source
• Ballistic transport and boundary resistances in inhomogeneous quantum spin chains
• Exact hydrodynamic description of symmetry-resolved Rényi entropies after a quantum quench
• Front dynamics in the XY chain after local excitations
• Exact large deviation function of spin current for the one dimensional XX spin chain with domain wall initial condition
• Quantum dynamics of impenetrable SU(N) fermions in one-dimensional lattices
• Family-Vicsek dynamical scaling and Kardar-Parisi-Zhang-like superdiffusive growth of surface roughness in a driven one-dimensional quasiperiodic model
• Interface dynamics in the two-dimensional quantum Ising model
• Multilayered density profile for noninteracting fermions in a rotating two-dimensional trap
• Dynamics and level statistics of interacting fermions in the Lowest Landau Level
• Disorder-induced Enhancement of Entanglement Growth in One Dimension: Information Leakage at the scale of localization length
• Generalized-Hydrodynamic approach to Inhomogeneous Quenches: Correlations, Entanglement and Quantum Effects
• Domain wall melting in spin-1 chains
• Quench dynamics of noninteracting fermions with a delta impurity
• Exact time evolution formulae in the XXZ spin chain with domain wall initial state
• Current fluctuations in the Dyson Gas
• Domain wall dynamics in classical spin chains: free propagation, subdiffusive spreading, and soliton emission
• Exact density profile in a tight-binding chain with dephasing noise
• Non-probabilistic fermionic limit shapes
• On Landauer--Büttiker formalism from a quantum quench
• Irreversible Reactions and Diffusive Escape: Stationary Properties
• Quasicondensation and off-diagonal long-range order of hard-core bosons during a free expansion
• A hydrodynamic approach to Stark localization
• Ballistic conductance with and without disorder in a boundary-driven XXZ spin chain
• Domain-wall melting and entanglement in free-fermion chains with a band structure
• Entanglement dynamics of a hard-core quantum gas during a Joule expansion
• Entanglement Hamiltonian during a domain wall melting in the free Fermi chain
• Inhomogeneous quenches and GHD in the $\nu =1$ QSSEP model
• Domain-wall melting in all-to-all QSSEP from random-matrix theory