The Thouless time for mass-deformed SYK

• Main Authors: Tomoki Nosaka, Dario Rosa, Junggi Yoon
• Format: Article
• Language: English
• Published: SpringerOpen 2018-09-01
• Series: Journal of High Energy Physics
• Subjects: Matrix Models; Integrable Field Theories; Stochastic Processes; Black Holes
• Online Access: http://link.springer.com/article/10.1007/JHEP09(2018)041
• ISSN: 1029-8479

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 shows a closer agreement with the transition as seen by the OTOCs. We argue that the chaotic/integrable deformation affects 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.