Entanglement distribution in the quantum symmetric simple exclusion process.

Denis Bernard,Lorenzo Piroli

doi:10.1103/physreve.104.014146

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 we focus on the late-time distribution of Rényi-q entropies for a subsystem of size ℓ. 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 ℓ/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.

Highlights

Many physical phenomena admit a description in terms of random variables, whose dynamics is dictated by stochastic processes
Using the Coulomb gas (CG) approach from random matrix theory (RMT), we find that it displays distinct phases, with two of them corresponding to states approaching either a pure state or a maximally mixed one
These regimes are separated by critical points where the probability density features singularities in its third derivative and which can be understood in terms of a transition in the corresponding charge density of the CG

Summary

INTRODUCTION

Many physical phenomena admit a description in terms of random variables, whose dynamics is dictated by stochastic processes. We initiate a series of investigations aimed at understanding entanglement fluctuations in a prototypical model for quantum many-body stochastic dynamics: the quantum simple symmetric exclusion process (Q-SSEP), cf Fig. 1. Using the Coulomb gas (CG) approach from random matrix theory (RMT), we find that it displays distinct phases, with two of them corresponding to states approaching either a pure state or a maximally mixed one (defining regimes of low and high entanglement, respectively) These regimes are separated by critical points where the probability density features singularities in its third derivative and which can be understood in terms of a transition in the corresponding charge density of the CG.

THE MODEL

THE COULOMB GAS APPROACH

THE EXACT SOLUTION

CONCLUSIONS