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From Chaos to Integrability in Double Scaled Sachdev-Ye-Kitaev Model via a Chord Path Integral
Micha Berkooz1, Nadav Brukner1, Yiyang Jia1
1Department of Particle Physics and Astrophysics, <a href="https://ror.org/0316ej306">Weizmann Institute of Science</a>, Rehovot 7610001, Israel.
Physical Review Letters
|December 13, 2024
Summary
We explore thermodynamic phase transitions between integrable and chaotic dynamics using models interpolating between Sachdev-Ye-Kitaev (SYK) and p-spin systems. Our findings reveal two distinct phases separated by a first-order transition line ending at finite temperature.
Area of Science:
- Quantum mechanics
- Statistical mechanics
- Condensed matter physics
Background:
- Understanding the interplay between integrability and chaos is crucial in quantum systems.
- The Sachdev-Ye-Kitaev (SYK) model and p-spin systems represent archetypal chaotic and integrable models, respectively.
Purpose of the Study:
- To investigate thermodynamic phase transitions between integrable and chaotic dynamics.
- To analyze models interpolating between the chaotic double-scaled SYK model and integrable p-spin systems.
- To characterize the nature of the phase transition and its temperature dependence.
Main Methods:
- Analysis of models interpolating between chaotic (SYK) and integrable (p-spin) systems.
- Utilizing a limit where models are described by chord diagrams.
- Development of a path integral formalism by coarse-graining over diagrams.
Main Results:
- Identified two distinct phases in the system.
- One phase is continuously connected to the chaotic SYK dynamics.
- The other phase is continuously connected to the integrable p-spin dynamics.
- A line of first-order phase transitions separates these two phases.
- This transition line terminates at a finite temperature.
Conclusions:
- The studied models exhibit a clear distinction between integrable and chaotic dynamics.
- Thermodynamic phase transitions play a key role in governing the system's behavior.
- The identified first-order transition provides a mechanism for switching between integrability and chaos.
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