Thermodynamics and dynamics of coupled complex SYK models

• URL: http://arxiv.org/abs/2312.14644v3
• Date: Tue, 14 May 2024 11:00:25 GMT
• Title: Thermodynamics and dynamics of coupled complex SYK models
• Authors: Jan C. Louw, Linda M. van Manen, Rishabh Jha,
• Abstract summary: This work establishes the universality of this shared universality class and chaotic properties for SYK-like models. We demonstrate that the coupled SYK system remains maximally chaotic in the large-$q$ limit at low temperatures. These findings establish robustness and open avenues for broader inquiries into the universality and chaos in complex quantum systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: It has been known that the large-$q$ complex SYK model falls under the same universality class as that of van der Waals (mean-field) and saturates the Maldacena-Shenker-Stanford bound, both features shared by various black holes. This makes the SYK model a useful tool in probing the fundamental nature of quantum chaos and holographic duality. This work establishes the robustness of this shared universality class and chaotic properties for SYK-like models by extending to a system of coupled large-$q$ complex SYK models of different orders. We provide a detailed derivation of thermodynamic properties, specifically the critical exponents for an observed phase transition, as well as dynamical properties, in particular the Lyapunov exponent, via the out-of-time correlator calculations. Our analysis reveals that, despite the introduction of an additional scaling parameter through interaction strength ratios, the system undergoes a continuous phase transition at low temperatures, similar to that of the single SYK model. The critical exponents align with the Landau-Ginzburg (mean-field) universality class, shared with van der Waals gases and various AdS black holes. Furthermore, we demonstrate that the coupled SYK system remains maximally chaotic in the large-$q$ limit at low temperatures, adhering to the Maldacena-Shenker-Stanford bound, a feature consistent with the single SYK model. These findings establish robustness and open avenues for broader inquiries into the universality and chaos in complex quantum systems. We provide a detailed outlook for future work by considering the ``very" low-temperature regime, where we discuss relations with the Hawking-Page phase transition observed in the holographic dual black holes. We present preliminary calculations and discuss the possible follow-ups that might be be taken to make the connection robust.

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