Fluctuating hydrodynamics, current fluctuations and hyperuniformity in boundary-driven open quantum chains

Abstract

We consider a class of either fermionic or bosonic noninteracting open quantum chains driven by dissipative interactions at the boundaries and study the interplay of coherent transport and dissipative processes, such as bulk dephasing and diffusion. Starting from the microscopic formulation, we show that the dynamics on large scales can be described in terms of fluctuating hydrodynamics. This is an important simplification as it allows us to apply the methods of macroscopic fluctuation theory to compute the large deviation (LD) statistics of time-integrated currents. In particular, this permits us to show that fermionic open chains display a third-order dynamical phase transition in LD functions. We show that this transition is manifested in a singular change in the structure of trajectories: while typical trajectories are diffusive, rare trajectories associated with atypical currents are ballistic and hyperuniform in their spatial structure. We confirm these results by numerically simulating ensembles of rare trajectories via the cloning method, and by exact numerical diagonalization of the microscopic quantum generator.

14 pages + 3 figures

References in corpus (25)

• Many body localization and thermalization in quantum statistical mechanics
• The large deviation approach to statistical mechanics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Experimental Observation of a Generalized Gibbs Ensemble
• Dynamic first-order phase transition in kinetically constrained models of glasses
• Spin diffusion from an inhomogeneous quench in an integrable system
• Quantum limit of heat flow across a single electronic channel
• Signatures of Many-Body Localization in a Controlled Open Quantum System
• Equilibration and Order in Quantum Floquet Matter
• Hyperuniformity and its Generalizations
• A numerical approach to large deviations in continuous-time
• Hyperuniformity and phase separation in biased ensembles of trajectories for diffusive systems
• Large deviations and universality in quantum quenches
• Mapping out of equilibrium into equilibrium in one-dimensional transport models
• Solvable quantum nonequilibrium model exhibiting a phase transition and a matrix product representation
• Measuring the dynamic structure factor of a quantum gas undergoing a structural phase transition
• Dynamical symmetry breaking and phase transitions in driven diffusive systems
• Generic Dynamical Phase Transition in One-Dimensional Bulk-Driven Lattice Gases with Exclusion
• A matrix product solution for a nonequilibrium steady state of an XX chain
• Solution of the Lindblad equation for spin helix states
• Exact steady state manifold of a boundary driven spin-1 Lai-Sutherland chain
• Boundary-driven Lindblad dynamics of random quantum spin chains : strong disorder approach for the relaxation, the steady state and the current
• Dissipation-driven integrable fermionic systems: from graded Yangians to exact nonequilibrium steady states
• Dissipative random quantum spin chain with boundary-driving and bulk-dephasing: magnetization and current statistics in the Non-Equilibrium-Steady-State
• Matrix product ansatz for non-equilibrium quantum steady states

Cited by in corpus (42)

• Entanglement in a fermion chain under continuous monitoring
• Unravelling the large deviation statistics of Markovian open quantum systems
• Growth of entanglement entropy under local projective measurements
• Making rare events typical in Markovian open quantum systems
• Open Quantum Symmetric Simple Exclusion Process
• Fluctuations in ballistic transport from Euler hydrodynamics
• Nonlinear sigma models for monitored dynamics of free fermions
• Transport fluctuations in integrable models out of equilibrium
• Generalised hydrodynamics with dephasing noise
• Stochastic dissipative quantum spin chains (I) : Quantum fluctuating discrete hydrodynamics
• Harnessing symmetry to control quantum transport
• Enhanced entanglement negativity in boundary driven monitored fermionic chains
• Full counting statistics as probe of measurement-induced transitions in the quantum Ising chain
• Building continuous time crystals from rare events
• From stochastic spin chains to quantum Kardar-Parisi-Zhang dynamics
• Transport in quantum chains under strong monitoring
• Sampling rare events across dynamical phase transitions
• Current fluctuations in boundary-driven quantum spin chains
• Free Fermions with a Localized Source
• Monitored fermions with conserved $\mathrm{U}(1)$ charge
• Dynamics of large deviations in the hydrodynamic limit: Non-interacting systems
• Phases of quantum dimers from ensembles of classical stochastic trajectories
• Efficient characterisation of large deviations using population dynamics
• Exponential size scaling of the Liouvillian gap in boundary-dissipated systems with Anderson localization
• Bath assisted transport in a three-site spin chain: global {\sl vs} local approach
• Non-equilibrium dynamic hyperuniform states
• The kinetic exclusion process: a tale of two fields
• Coupled activity-current fluctuations in open quantum systems under strong symmetries
• Dynamical criticality in open systems: non-perturbative physics, microscopic origin and direct observation
• Exact steady state of the open XX-spin chain: entanglement and transport properties
• Dynamical phase transition to localized states in the two-dimensional random walk conditioned on partial currents
• Finite-size and finite-time effects in large deviation functions near dynamical symmetry breaking transitions
• Singularities in large deviations of work in quantum quenches
• Manipulating the Relaxation Time of Boundary-Dissipative Systems through Bond Dissipation
• Exact density profile in a tight-binding chain with dephasing noise
• Non-equilibrium boundary driven quantum systems: models, methods and properties
• Dynamics of entanglement fluctuations and quantum Mpemba effect in the $\nu =1$ QSSEP model
• Diffusion and entanglement in open quantum systems
• Devitrification and Melting Dynamics in Vapor Deposited Water Ice
• Ballistic conductance with and without disorder in a boundary-driven XXZ spin chain
• Transfer matrix approach to quantum systems subject to certain Lindblad evolution
• Mapping current and activity fluctuations in exclusion processes: consequences and open questions