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Many-Body Chaos in the Sachdev-Ye-Kitaev Model
Bryce Kobrin1,2, Zhenbin Yang3,4, Gregory D Kahanamoku-Meyer1
1Department of Physics, University of California, Berkeley, California 94720, USA.
Physical Review Letters
|February 5, 2021
Summary
Many-body chaos in quantum systems is explored using advanced numerical methods. This study precisely measures the Lyapunov exponent, a key indicator of chaos, across various temperatures.
Area of Science:
- Quantum mechanics
- Statistical mechanics
- Condensed matter physics
Background:
- Many-body chaos is crucial for understanding thermalization in strongly interacting quantum systems.
- Analytic methods for many-body chaos are limited to specific theories, necessitating new numerical approaches.
- Previous numerical tools struggled to explore chaos in generic Hamiltonians.
Purpose of the Study:
- To develop precise numerical tools for studying many-body chaos in generic quantum systems.
- To calculate dynamical correlators and the Lyapunov exponent in the Sachdev-Ye-Kitaev model.
- To validate numerical findings against theoretical predictions and explore finite-size effects.
Main Methods:
- Utilized massively parallel, matrix-free Krylov subspace methods.
- Calculated dynamical correlators for the Sachdev-Ye-Kitaev model with up to N=60 Majorana fermions.
- Developed a novel finite-size rescaling procedure for analyzing out-of-time-order correlators.
Main Results:
- Numerical results for two-point correlation functions align with dynamical mean-field solutions at high temperatures.
- Finite-size corrections at low temperatures match predictions from near extremal black hole dynamics.
- Accurately determined the Lyapunov exponent across a broad temperature range, including near the universal bound (λ=2π/β).
Conclusions:
- The developed numerical methods provide a powerful tool for investigating many-body chaos.
- The study confirms the applicability of the Sachdev-Ye-Kitaev model in understanding thermalization.
- The findings offer insights into the universal behavior of chaos in quantum systems.
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