Entanglement distribution in the Quantum Symmetric Simple Exclusion Process

• URL: http://arxiv.org/abs/2102.04745v2
• Date: Mon, 26 Jul 2021 13:04:54 GMT
• Title: Entanglement distribution in the Quantum Symmetric Simple Exclusion Process
• Authors: Denis Bernard, Lorenzo Piroli
• Abstract summary: We study the probability distribution of entanglement in the Quantum Symmetric Simple Exclusion Process. 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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