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Nonergodic Extended States in the Sachdev-Ye-Kitaev Model.
T Micklitz1, Felipe Monteiro1, Alexander Altland2
1Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180, Rio de Janeiro, Brazil.
Physical Review Letters
|October 22, 2019
Summary
We studied quantum systems and found that spectral statistics can be Wigner-Dyson type even when wave functions are not uniformly distributed. This suggests nonergodic extendedness is common in chaotic quantum systems.
Area of Science:
- Quantum mechanics
- Statistical physics
- Condensed matter theory
Background:
- The Sachdev-Ye-Kitaev (SYK) model is a pivotal model in quantum chaos and black hole physics.
- Understanding spectral correlations and wave function distributions is crucial for characterizing quantum chaotic systems.
Purpose of the Study:
- To analytically investigate the spectral correlations and many-body wave functions of the SYK model.
- To explore the impact of random Hamiltonian perturbations on these properties.
- To identify conditions leading to nonergodic extendedness in quantum chaotic systems.
Main Methods:
- Analytical study of the SYK model.
- Inclusion of a random Hamiltonian diagonal in Fock space.
- Analysis of spectral statistics and wave function distribution over Fock space.
Main Results:
- Identified a broad range of intermediate coupling strengths exhibiting Wigner-Dyson type spectral statistics.
- Observed nonuniform distribution of wave functions over Fock space within this regime.
- The findings highlight a coexistence of seemingly contradictory properties in quantum chaotic systems.
Conclusions:
- Nonergodic extendedness, characterized by Wigner-Dyson statistics and non-uniform wave functions, is a significant phenomenon.
- This manifestation of nonergodic extendedness is likely prevalent in various many-body chaotic quantum systems.
- The study provides insights into the complex nature of quantum chaos and its implications.
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