Thouless time for mass-deformed SYK

TL;DR

This paper investigates how the mass deformation in the SYK model influences the transition from chaotic to integrable behavior, using spectral form factors and OTOCs as probes, revealing inhomogeneous effects on energy levels.

Contribution

It introduces a detailed analysis of the mass-deformed SYK model's transition to integrability using novel spectral form factor techniques and compares different chaos indicators.

Findings

Gaussian-filtered SFF detects transition at large mass deformation

Connected unfolded SFF detects transition at small mass deformation

Low-lying states are affected at small deformation, bulk states at large deformation

Abstract

We study the onset of RMT dynamics in the mass-deformed SYK model (i.e. an SYK model deformed by a quadratic random interaction) in terms of the strength of the quadratic deformation. We use as chaos probes both the connected unfolded Spectral Form Factor (SFF) as well as the Gaussian-filtered SFF, which has been recently introduced in the literature. We show that they detect the chaotic/integrable transition of the mass-deformed SYK model at different values of the mass deformation: the Gaussian-filtered SFF sees the transition for large values of the mass deformation; the connected unfolded SFF sees the transition at small values. The latter is in qualitative agreement with the transition as seen by the OTOCs. We argue that the chaotic/integrable deformation affect the energy levels inhomogeneously: for small values of the mass deformation only the low-lying states are modified while for large values of the mass deformation also the states in the bulk of the spectrum move to the integrable behavior.