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

Wouter Buijsman; Vadim Cheianov; Vladimir Gritsev

doi:10.1103/physreve.102.042216

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arXiv · 2009.02249

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

Wouter Buijsman·Vadim Cheianov·Vladimir Gritsev

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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.

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Wouter Buijsman, Vadim Cheianov, Vladimir Gritsev. 2020-09-04. Sensitivity of the spectral form factor to short-range level statistics. https://doi.org/10.1103/physreve.102.042216

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