From Chaos to Integrability in Double Scaled SYK via a Chord Path Integral
Abstract
We study thermodynamic phase transitions between integrable and chaotic dynamics. We do so by analyzing models that interpolate between the chaotic double scaled Sachdev-Ye-Kitaev (SYK) and the integrable -spin systems, in a limit where they are described by chord diagrams. We develop a path integral formalism by coarse graining over the diagrams, which we use to argue that the system has two distinct phases: one is continuously connected to the chaotic system, and the other to the integrable. They are separated by a line of first order transition that ends at some finite temperature.
Cite
@article{arxiv.2403.01950,
title = {From Chaos to Integrability in Double Scaled SYK via a Chord Path Integral},
author = {Micha Berkooz and Nadav Brukner and Yiyang Jia and Ohad Mamroud},
journal= {arXiv preprint arXiv:2403.01950},
year = {2024}
}
Comments
5+5 pages. Companion paper to 2403.05980. v2: added further details about the classification of the phases, including computation of Krylov complexity when the analytic approximations apply. Also added supplemental material