Inhomogeneous quenches and GHD in the $\nu =1$ QSSEP model

Abstract

We investigate the dynamics of the $\nu =1$ Quantum Symmetric Simple Exclusion Process starting from spatially inhomogeneous initial states. This one-dimensional system of free fermions has time-dependent stochastic hopping amplitudes that are uniform in space. We focus on two paradigmatic setups: domain-wall melting and the expansion of a trapped gas. Both are investigated by extending the framework of quantum generalized hydrodynamics to account for the underlying stochastic dynamics. We derive the evolution of the local quasiparticle occupation function, which characterizes the system at large space-time scales, and analyze the resulting entanglement spreading. By incorporating quantum fluctuations of the occupation function and employing conformal field theory techniques, we obtain the exact contribution to the entanglement entropy for each individual noise realization. Averaging over these realizations then yields the full entanglement statistics in the hydrodynamic regime. Our theoretical predictions are confirmed by exact numerical calculations. The results presented here constitute the first application of quantum generalized hydrodynamics to stochastic quantum systems, demonstrating that this framework can be successfully extended beyond purely unitary dynamics to include stochastic effects.

25 pages, 7 figures, final version published in JSTAT

References in corpus (36)

• Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
• Transport in out-of-equilibrium XXZ chains: non-ballistic behavior and correlation functions
• Full counting statistics in a propagating quantum front and random matrix spectra
• Generalized hydrodynamics in strongly interacting 1D Bose gases
• Entanglement asymmetry as a probe of symmetry breaking
• Higher-Order Hydrodynamics in 1D: a Promising Direction and a Null Result
• The Exclusion Process: A paradigm for non-equilibrium behaviour
• Logarithmic current fluctuations in non-equilibrium quantum spin chains
• Universal corrections to scaling for block entanglement in spin-1/2 XX chains
• Relaxation in the XX quantum chain
• Generalised hydrodynamics with dephasing noise
• Entanglement spreading in non-equilibrium integrable systems
• Conformal field theory on top of a breathing one-dimensional gas of hard core bosons
• A short introduction to Generalized Hydrodynamics
• Entanglement distribution in the Quantum Symmetric Simple Exclusion Process
• Generalized hydrodynamics: a perspective
• Coherent Fluctuations in Noisy Mesoscopic Systems, the Open Quantum SSEP and Free Probability
• Magnetization and entanglement after a geometric quench in the XXZ chain
• Dynamics of Fluctuations in Quantum Simple Exclusion Processes
• 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
• Wigner function for a particle in an infinite lattice
• Domain wall melting across a defect
• Can the Macroscopic Fluctuation Theory be Quantized?
• Scaling of fronts and entanglement spreading during a domain wall melting
• Spacetime picture for entanglement generation in noisy fermion chains
• One-particle density matrix and momentum distribution of the out-of-equilibrium 1D Tonks-Girardeau gas: Analytical results at large $N$
• Large deviations of density fluctuations in the boundary driven Quantum Symmetric Simple Inclusion Process
• Experimental Investigation of a Bipartite Quench in a 1D Bose gas
• Dynamics of entanglement fluctuations and quantum Mpemba effect in the $\nu =1$ QSSEP model
• A hydrodynamic approach to Stark localization
• $\nu$-QSSEP: A toy model for entanglement spreading in stochastic diffusive quantum systems
• Quasicondensation and off-diagonal long-range order of hard-core bosons during a free expansion
• Domain-wall melting and entanglement in free-fermion chains with a band structure
• Enhanced correlations due to ballistic transport
• Analytical solution of a free-fermion chain with time-dependent ramps