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Many-body quantum chaos and space-time translational invariance.
Amos Chan1,2, Saumya Shivam3, David A Huse3
1Princeton Center for Theoretical Science, Princeton University, Princeton, NJ, 08544, USA. amos.chan@princeton.edu.
Nature Communications
|December 5, 2022
Summary
Translational invariance in quantum chaotic systems delays the emergence of random matrix theory (RMT) behavior. New Feynman diagrams reveal universal scaling functions describing this approach in the scaling limit.
Area of Science:
- Quantum physics
- Condensed matter theory
- Statistical mechanics
Background:
- Many-body quantum chaotic systems exhibit complex dynamics.
- Translational invariance is a fundamental symmetry in physical systems.
- Random matrix theory (RMT) describes spectral properties of chaotic systems.
Purpose of the Study:
- Investigate the impact of translational invariance on quantum chaotic systems.
- Analyze the spectral form factor in models with this symmetry.
- Understand deviations from RMT behavior.
Main Methods:
- Utilized ensembles of random quantum circuits as minimal models.
- Evaluated the spectral form factor using many-body Feynman diagrams.
- Analyzed the limit of large local Hilbert space dimension (q).
- Employed analytical techniques and numerical simulations.
Main Results:
- Identified novel Feynman diagrams arising from translational invariance.
- Demonstrated that these diagrams delay the onset of RMT behavior.
- Derived exact scaling forms for the approach to RMT.
- Confirmed universality of scaling functions in the scaling limit through simulations.
Conclusions:
- Translational invariance introduces unique mechanisms affecting spectral statistics.
- The study provides a framework for understanding deviations from RMT in physical systems.
- Numerical evidence supports the universality of the observed scaling behavior.
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