Sensitivity of the spectral form factor to short-range level statistics

TL;DR

This paper investigates how the spectral form factor's early-time behavior is influenced by short-range level statistics and proposes a new probe to better interpret spectral correlations in quantum systems.

Contribution

It introduces a new spectral form factor probe that removes self-correlation constraints, improving the analysis of level statistics and ergodicity in quantum models.

Findings

The spectral form factor is constrained by self-correlation effects.

A new probe effectively isolates short-range level statistics.

Application to models shows improved interpretation of spectral data.

Abstract

The spectral form factor is a dynamical probe for level statistics of quantum systems. The early-time behaviour is commonly interpreted as a characterization of two-point correlations at large separation. We argue that this interpretation can be too restrictive by indicating that the self-correlation imposes a constraint on the spectral form factor integrated over time. More generally, we indicate that each expansion coefficient of the two-point correlation function imposes a constraint on the properly weighted time-integrated spectral form factor. We discuss how these constraints can affect the interpretation of the spectral form factor as a probe for ergodicity. We propose a new probe, which eliminates the effect of the constraint imposed by the self-correlation. The use of this probe is demonstrated for a model of randomly incomplete spectra and a Floquet model supporting many-body localization.