Random Matrix Statistics in Propagating Correlation Fronts of Fermions

TL;DR

This paper reveals a universal connection between the statistical properties of propagating correlation fronts in non-interacting fermions and Gaussian orthogonal and symplectic random matrix ensembles, bridging quantum dynamics and random matrix theory.

Contribution

It uncovers a novel link between random matrix statistics and correlation front propagation in quantum fermionic systems, expanding understanding of quantum dynamics.

Findings

Moments of fluctuations follow universal random matrix correlations

Correlation fronts exhibit Gaussian orthogonal and symplectic statistics

Establishes a new connection between quantum dynamics and random matrix theory

Abstract

We theoretically study propagating correlation fronts in non-interacting fermions on a one-dimensional lattice starting from an alternating state, where the fermions occupy every other site. We find that, in the long-time asymptotic regime, all the moments of dynamical fluctuations around the correlation fronts are described by the universal correlation functions of Gaussian orthogonal and symplectic random matrices at the soft edge. Our finding here sheds light on a hitherto unknown connection between random matrix theory and correlation propagation in quantum dynamics.