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arXiv · 1804.09934

Thouless time for mass-deformed SYK

Tomoki Nosaka·Dario Rosa·Junggi Yoon
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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.

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Tomoki Nosaka, Dario Rosa, Junggi Yoon. 2018-04-26. Thouless time for mass-deformed SYK. https://doi.org/10.1007/jhep09(2018)041

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