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arXiv · 2403.05980

A Path Integral for Chord Diagrams and Chaotic-Integrable Transitions in Double Scaled SYK

Micha Berkooz·Nadav Brukner·Yiyang Jia·Ohad Mamroud
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Abstract

We study transitions from chaotic to integrable Hamiltonians in the double scaled SYK and $p$-spin systems. The dynamics of our models is described by chord diagrams with two species. We begin by developing a path integral formalism of coarse graining chord diagrams with a single species of chords, which has the same equations of motion as the bi-local ($G\Sigma$) Liouville action, yet appears otherwise to be different and in particular well defined. We then develop a similar formalism for two types of chords, allowing us to study different types of deformations of double scaled SYK and in particular a deformation by an integrable Hamiltonian. The system has two distinct thermodynamic phases: one is continuously connected to the chaotic SYK Hamiltonian, the other is continuously connected to the integrable Hamiltonian, separated at low temperature by a first order phase transition. We also analyze the phase diagram for generic deformations, which in some cases includes a zero-temperature phase transition.

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Micha Berkooz, Nadav Brukner, Yiyang Jia, Ohad Mamroud. 2024-03-09. A Path Integral for Chord Diagrams and Chaotic-Integrable Transitions in Double Scaled SYK. https://arxiv.org/abs/2403.05980

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