Entanglement distribution in the Quantum Symmetric Simple Exclusion Process

TL;DR

This paper analyzes the probability distribution of entanglement in a quantum fermionic model using Random Matrix Theory, revealing phase transitions in entropy distribution regimes and supporting findings with numerical simulations.

Contribution

It introduces an analytical Coulomb gas approach to compute large-deviation functions of entanglement entropy in the Quantum Symmetric Simple Exclusion Process, uncovering regime transitions.

Findings

Entropy distribution exhibits two or three regimes depending on subsystem size.

Transitions in the distribution are marked by singularities in the third derivative.

Numerical simulations confirm the analytical large-deviation results.

Abstract

We study the probability distribution of entanglement in the Quantum Symmetric Simple Exclusion Process, a model of fermions hopping with random Brownian amplitudes between neighboring sites. We consider a protocol where the system is initialized in a pure product state of $M$ particles, and focus on the late-time distribution of R\'enyi-$q$ entropies for a subsystem of size $\ell$. By means of a Coulomb gas approach from Random Matrix Theory, we compute analytically the large-deviation function of the entropy in the thermodynamic limit. For $q>1$, we show that, depending on the value of the ratio $\ell/M$, the entropy distribution displays either two or three distinct regimes, ranging from low- to high-entanglement. These are connected by points where the probability density features singularities in its third derivative, which can be understood in terms of a transition in the corresponding charge density of the Coulomb gas. Our analytic results are supported by numerical Monte Carlo simulations.