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Chaotic-Integrable Transition in the Sachdev-Ye-Kitaev Model.
Antonio M García-García1, Bruno Loureiro2, Aurelio Romero-Bermúdez3
1Shanghai Center for Complex Physics, Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China.
Physical Review Letters
|June 30, 2018
Summary
The Sachdev-Ye-Kitaev (SYK) model remains quantum chaotic with added interactions, but a transition to an integrable state occurs at a specific temperature. This transition depends on the perturbation strength and impacts holographic properties.
Area of Science:
- Quantum Field Theory
- Condensed Matter Physics
- High Energy Physics
Background:
- The Sachdev-Ye-Kitaev (SYK) model describes N Majorana fermions with infinite-range interactions, serving as a toy model for holography.
- Quantum chaos is a key feature of the SYK model, with applications in understanding black holes and quantum gravity.
Purpose of the Study:
- To investigate the impact of a relevant infrared perturbation (one-body random interaction) on the quantum chaos and holographic properties of the SYK model.
- To identify the conditions and characteristics of a potential chaotic-integrable transition in the generalized SYK model.
Main Methods:
- Analytical calculations to study the model's behavior under the perturbation.
- Numerical simulations to confirm analytical predictions and explore the parameter space.
- Analysis of Lyapunov exponents and spectral correlations to characterize chaos and integrability.
Main Results:
- The generalized SYK model exhibits quantum chaos and retains holographic features at high temperatures for a fixed perturbation.
- A transition from quantum chaos to an integrable state occurs at a temperature dependent on the perturbation strength.
- The transition is marked by the vanishing of the Lyapunov exponent and a change in spectral correlations to Poisson statistics.
Conclusions:
- The addition of a one-body random interaction perturbs the SYK model but preserves its chaotic nature and holographic dual at high temperatures.
- A critical temperature exists where the system transitions from a chaotic to an integrable regime, offering insights into quantum chaos.
- Further investigation into the gravity dual of this chaotic-integrable transition is warranted.
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