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

TL;DR

This paper extends quantum generalized hydrodynamics to stochastic quantum systems, analyzing inhomogeneous quenches in the $ u=1$ QSSEP model, and provides exact entanglement entropy results confirmed by numerical calculations.

Contribution

It introduces the first application of quantum GHD to stochastic quantum dynamics, deriving entanglement evolution in inhomogeneous quenches with noise.

Findings

Quantum GHD can be extended to stochastic systems.

Exact entanglement entropy contributions are obtained.

Numerical results confirm theoretical predictions.

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.