Random matrix theory signatures in free field theory

TL;DR

This paper demonstrates that random matrix theory signatures appear in free scalar field theory observables after a local quench, revealing RMT-like statistics in specific local measurements.

Contribution

It uncovers RMT signatures in free field theory observables post-quench, highlighting the emergence of RMT statistics in a non-interacting quantum field context.

Findings

Spacing-ratio distribution matches GOE statistics.

Extrema-based form factor shows dip-ramp-plateau RMT pattern.

Standard spectral form factor lacks a ramp, indicating free spectrum behavior.

Abstract

We show that, within a finite window of parameter space, random matrix theory (RMT) statistics emerge in observables of a finite-volume massive free scalar field theory after a local operator quench. The spacing-ratio distribution of two-point-function extremum locations is close to the Gaussian orthogonal ensemble statistics. An extrema-based form factor exhibits a dip--ramp--plateau structure characteristic of RMT. By contrast, the standard spectral form factor shows no ramp, consistent with the underlying free spectrum, while a global quench yields qualitatively different statistics.