Dynamics of Fluctuations in Quantum Simple Exclusion Processes

Abstract

We consider the dynamics of fluctuations in the quantum asymmetric simple exclusion process (Q-ASEP) with periodic boundary conditions. The Q-ASEP describes a chain of spinless fermions with random hoppings that are induced by a Markovian environment. We show that fluctuations of the fermionic degrees of freedom obey evolution equations of Lindblad type, and derive the corresponding Lindbladians. We identify the underlying algebraic structure by mapping them to non-Hermitian spin chains and demonstrate that the operator space fragments into exponentially many (in system size) sectors that are invariant under time evolution. At the level of quadratic fluctuations we consider the Lindbladian on the sectors that determine the late time dynamics for the particular case of the quantum symmetric simple exclusion process (Q-SSEP). We show that the corresponding blocks in some cases correspond to known Yang-Baxter integrable models and investigate the level-spacing statistics in others. We carry out a detailed analysis of the steady states and slow modes that govern the late time behaviour and show that the dynamics of fluctuations of observables is described in terms of closed sets of coupled linear differential-difference equations. The behaviour of the solutions to these equations is essentially diffusive but with relevant deviations, that at sufficiently late times and large distances can be described in terms of a continuum scaling limit which we construct. We numerically check the validity of this scaling limit over a significant range of time and space scales. These results are then applied to the study of operator spreading at large scales, focusing on out-of-time ordered correlators and operator entanglement.

arXiv comment66 pages, 12 figures

References in corpus (75)

• A bound on chaos
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Quantum Inverse Scattering Method and Correlation Functions
• Operator Spreading in Random Unitary Circuits
• Measurement-Induced Phase Transitions in the Dynamics of Entanglement
• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Macroscopic fluctuation theory
• Phase transitions in an exactly soluble one-dimensional exclusion process
• Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Spin transport in a one-dimensional anisotropic Heisenberg model
• Nonlinear fluctuating hydrodynamics for anharmonic chains
• Hydrodynamic Diffusion in Integrable Systems
• Local random quantum circuits are approximate polynomial-designs
• Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems
• Entanglement of Quantum Evolutions
• Solution of a minimal model for many-body quantum chaos
• Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
• Diffusive and subdiffusive spin transport in the ergodic phase of a many-body localizable system
• Macroscopic current fluctuations in stochastic lattice gases
• Thermalization near integrability in a dipolar quantum Newton's cradle
• Operator space entanglement entropy in transverse Ising chain
• Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
• Velocity-dependent Lyapunov exponents in many-body quantum, semi-classical, and classical chaos
• Exact Bethe ansatz spectrum of a tight-binding chain with dephasing noise
• Poisson versus GOE statistics in integrable and non-integrable quantum hamiltonian
• Dissipative Dynamics and Phase Transitions in Fermionic Systems
• Entanglement scaling of operators: a conformal field theory approach, with a glimpse of simulability of long-time dynamics in 1+1d
• Is efficiency of classical simulations of quantum dynamics related to integrability?
• Exact Liouvillian Spectrum of a One-Dimensional Dissipative Hubbard Model
• Dissipative spin chain as a non-Hermitian Kitaev ladder
• Operator entanglement entropy of the time evolution operator in chaotic systems
• Operator Space Entanglement Entropy in XY Spin Chains
• Spreading of correlations in Markovian open quantum systems
• Operator growth and eigenstate entanglement in an interacting integrable Floquet system
• Accessing scrambling using matrix product operators
• Decoupling with random quantum circuits
• Density Matrix Renormalization Group in the Heisenberg Picture
• Holographic Spacetimes as Quantum Circuits of Path-Integrations
• Constructing Integrable Lindblad Superoperators
• Open Quantum Symmetric Simple Exclusion Process
• Current large deviation function for the open asymmetric simple exclusion process
• An Exact Formula for the Statistics of the Current in the TASEP with Open Boundaries
• Complexity of thermal states in quantum spin chains
• Integrability of $1D$ Lindbladians from operator-space fragmentation
• Stochastic dissipative quantum spin chains (I) : Quantum fluctuating discrete hydrodynamics
• Entangling power of time-evolution operators in integrable and nonintegrable many-body systems
• Dissipative quantum Ising chain as a non-Hermitian Ashkin-Teller model
• Yang-Baxter integrable Lindblad equations
• Entanglement growth in diffusive systems
• Matrix Coordinate Bethe Ansatz: Applications to XXZ and ASEP models
• Some Exact Results for the Exclusion Process
• Equilibrium Fluctuations in Maximally Noisy Extended Quantum Systems
• Integrable quantum dynamics of open collective spin models
• Integrable impurity in the supersymmetric t-J model
• Noisy Coupled Qubits: Operator Spreading and the Fredrickson-Andersen Model
• Dynamical simulation of integrable and non-integrable models in the Heisenberg picture
• Level Statistics of XXZ Spin Chains with Discrete Symmetries: Analysis through Finite-size Effects
• Transport in a one-dimensional isotropic Heisenberg model at high temperature
• Long-lived non-thermal states realized by atom losses in one-dimensional quasi-condensates
• Universal power law in crossover from integrability to quantum chaos
• Diffusion and operator entanglement spreading
• From stochastic spin chains to quantum Kardar-Parisi-Zhang dynamics
• Transport in quantum chains under strong monitoring
• Signature of quantum chaos in operator entanglement in 2d CFTs
• Mixing times and cutoffs in open quadratic fermionic systems
• Solving the Liouvillian Gap with Artificial Neural Networks
• Weak integrability breaking and level spacing distribution
• Solution to the Quantum Symmetric Simple Exclusion Process : the Continuous Case
• Entanglement spectrum of mixed states
• Dissipative Bethe Ansatz: Exact Solutions of Quantum Many-Body Dynamics Under Loss
• Duality in quantum transport models
• Trigonometric SU(N) Richardson-Gaudin models and dissipative multi-level atomic systems
• Exact solution of a quantum asymmetric exclusion process with particle creation and annihilation

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• Theory of free fermions under random projective measurements
• Enhanced entanglement negativity in boundary driven monitored fermionic chains
• Ballistic macroscopic fluctuation theory
• Symmetry-resolved Page curves
• Coherent Fluctuations in Noisy Mesoscopic Systems, the Open Quantum SSEP and Free Probability
• Full Counting Statistics of Charge in Chaotic Many-body Quantum Systems
• Measurement-induced transitions for interacting fermions
• Monitored fermions with conserved $\mathrm{U}(1)$ charge
• Designs via Free Probability
• Symmetries as Ground States of Local Superoperators: Hydrodynamic Implications
• Stochastic Operator Variance: an observable to diagnose noise and scrambling
• Universal out-of-equilibrium dynamics of 1D critical quantum systems perturbed by noise coupled to energy
• Spacetime picture for entanglement generation in noisy fermion chains
• Ballistic Modes as a Source of Anomalous Charge Noise
• Non-Bloch dynamics and topology in a classical non-equilibrium process
• Effects of Quantum Pair Creation and Annihilation on a Classical Exclusion Process: the transverse XY model with TASEP
• Noise Induced Universal Diffusive Transport in Fermionic Chains
• Dynamics of entanglement fluctuations and quantum Mpemba effect in the $\nu =1$ QSSEP model
• $\nu$-QSSEP: A toy model for entanglement spreading in stochastic diffusive quantum systems
• Linear response and exact hydrodynamic projections in Lindblad equations with decoupled Bogoliubov hierarchies
• Dynamics in the presence of local symmetry-breaking impurities
• Entanglement dynamics from universal low-lying modes
• Inhomogeneous quenches and GHD in the $\nu =1$ QSSEP model
• Nonequilibrium phases and quantum correlations in synthetic transport models
• Domain-wall melting in all-to-all QSSEP from random-matrix theory