Domain-wall melting in all-to-all QSSEP from random-matrix theory

TL;DR

This paper analyzes the domain-wall melting in an all-to-all quantum exclusion process using random matrix theory, deriving explicit dynamics for eigenvalues, entanglement entropy, and charge statistics.

Contribution

It introduces a novel approach linking spectral results from random matrix theory to the dynamics of a quantum exclusion process with all-to-all interactions.

Findings

Eigenvalues evolve according to a Jacobi process.

Explicit expression for von Neumann entanglement entropy in the thermodynamic limit.

Quantum and classical full-counting statistics coincide in the thermodynamic limit.

Abstract

We study the melting of a domain wall in the quantum simple exclusion process with all-to-all hoppings (a.k.a. the charged SYK$_2$ model). We show that the real-time dynamics of physical quantities of interest can be obtained exploiting spectral results in random matrix theory. We first show that the eigenvalues of the correlation matrix corresponding to the initially charged subsystem evolve according to a Jacobi process, which is defined in terms of a closed system of stochastic differential equations. In turn, this observation allows us to obtain the real-time dynamics of all the eigenvalue moments. We present two physical applications. First, we study the dynamics of the averaged von Neumann entanglement entropy, arriving at a fully explicit expression in the thermodynamic limit. Second, we compute analytically the full-counting statistics of the charge. Our formula allows us to perform a thorough comparison with the full-counting statistics of the classical simple exclusion process. Notably, we show that, in the thermodynamic limit, the quantum and classical full-counting statistics coincide, with no finite-time corrections.