$\nu$-QSSEP: A toy model for entanglement spreading in stochastic diffusive quantum systems

TL;DR

This paper studies entanglement spreading in a stochastic free-fermion model with spatially-modulated noise, revealing diffusive growth and topological correlations in steady states.

Contribution

It introduces a generalized $QSSEP$ model with spatially-modulated noise, analyzing entanglement dynamics and topological properties of steady-state correlators.

Findings

Entanglement propagates via quasiparticles with random walk trajectories.

Diffusive entanglement growth observed for spatially homogeneous noise.

Steady-state correlators exhibit topological relationships related to Haar invariance.

Abstract

We investigate out-of-equilibrium entanglement dynamics in a generalization of the so-called $QSSEP$ model, which is a free-fermion chain with stochastic in space and time hopping amplitudes. In our setup, the noisy amplitudes are spatially-modulated satisfying a $\nu$-site translation invariance but retaining their randomness in time. For each noise realization, the dynamics preserves Gaussianity, which allows to obtain noise-averaged entanglement-related quantities. The statistics of the steady-state correlators satisfy nontrivial relationships that are of topological nature. They reflect the Haar invariance under multiplication with structured momentum-dependent random $SU(\nu)$ matrices. We discuss in detail the case with $\nu=1$ and $\nu=2$. For $\nu=1$, i.e., spatially homogeneous noise we show that the entanglement dynamics is describable by a stochastic generalization of the quasiparticle picture. Precisely, entanglement is propagated by pairs of quasiparticles. The entanglement content of the pairs is the same as for the deterministic chain. However, the trajectories of the quasiparticles are random walks, giving rise to diffusive entanglement growth.