Dissipative random quantum spin chain with boundary-driving and bulk-dephasing: magnetization and current statistics in the Non-Equilibrium-Steady-State

Abstract

The Lindblad dynamics with dephasing in the bulk and magnetization-driving at the two boundaries is studied for the quantum spin chain with random fields $h_j$ and couplings $J_j$ (that can be either uniform or random). In the regime of strong disorder in the random fields, or in the regime of strong bulk-dephasing, the effective dynamics can be mapped onto a classical Simple Symmetric Exclusion Process with quenched disorder in the diffusion coefficient associated to each bond. The properties of the corresponding Non-Equilibrium-Steady-State in each disordered sample between the two reservoirs are studied in detail by extending the methods that have been previously developed for the Symmetric Exclusion Process without disorder. Explicit results are given for the magnetization profile, for the two-point correlations, for the mean current and for the current fluctuations, in terms of the random fields and couplings defining the disordered sample.

revised version, 17 pages

References in corpus (15)

• Many body localization and thermalization in quantum statistical mechanics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems
• Charge and spin transport in strongly correlated one-dimensional quantum systems driven far from equilibrium
• Solvable quantum nonequilibrium model exhibiting a phase transition and a matrix product representation
• Diffusive high-temperature transport in the one-dimensional Hubbard model
• Two-time Correlations Probing the Dynamics of Dissipative Many-Body Quantum Systems: Aging and Fast Relaxation
• Transport in a disordered tight-binding chain with dephasing
• Negative differential conductivity in far-from-equilibrium quantum spin chains
• Metastability in an open quantum Ising model
• A matrix product solution for a nonequilibrium steady state of an XX chain
• The open Heisenberg chain under boundary fields: a magnonic logic gate
• Anomalous nonequilibrium current fluctuations in the Heisenberg model
• Exact asymptotics of the current in boundary dissipated quantum chains in large external fields

Cited by in corpus (13)

• Strong Disorder RG approach - a short review of recent developments
• Fluctuating hydrodynamics, current fluctuations and hyperuniformity in boundary-driven open quantum chains
• Exact description of quantum stochastic models as quantum resistors
• Describing many-body localized systems in thermal environments
• Criteria for Davies Irreducibility of Markovian Quantum Dynamics
• Boundary driven Heisenberg-chain in the long-range interacting regime: Robustness against far from equilibrium effects
• Quantum information spreading in random spin chains
• Charge and spin current statistics of the open Hubbard model with weak coupling to the environment
• Long-range interaction in an open boundary-driven Heisenberg spin lattice: A far-from-equilibrium transition to ballistic transport
• Strongly correlated non-equilibrium steady states with currents --- quantum and classical picture
• Inhomogeneous asymmetric exclusion processes between two reservoirs : large deviations for the local empirical observables in the Mean-Field approximation
• Relaxation of imbalance in a disordered XX model with on-site dephasing
• Measurement-Induced Phase Transition in a Disordered XX Spin Chain: A Real-Space Renormalization Group Study