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Spectral Statistics in Spatially Extended Chaotic Quantum Many-Body Systems
Amos Chan1, Andrea De Luca1, J T Chalker1
1Theoretical Physics, Oxford University, 1 Keble Road, Oxford OX1 3NP, United Kingdom.
Physical Review Letters
|August 25, 2018
Summary
Spectral statistics in quantum many-body systems were analyzed. The study found that spatial dimension significantly impacts the many-body Thouless time, influencing deviations from random matrix theory predictions.
Area of Science:
- Quantum physics
- Condensed matter theory
- Statistical mechanics
Background:
- Chaotic quantum many-body systems exhibit complex spectral statistics.
- Random matrix theory (RMT) often describes these statistics.
- Lattice Floquet models provide a framework to study non-equilibrium quantum dynamics.
Purpose of the Study:
- Investigate spectral statistics in spatially extended chaotic quantum many-body systems.
- Analyze the behavior of the spectral form factor (K(t)).
- Determine the influence of spatial dimensions and system size on spectral correlations.
Main Methods:
- Utilized simple lattice Floquet models lacking time-reversal symmetry.
- Employed analytical and numerical computations of the spectral form factor K(t).
- Examined the many-body Thouless time (t_Th) and its dependence on system parameters.
Main Results:
- The spectral form factor K(t) aligns with RMT for times exceeding the many-body Thouless time (t_Th).
- t_Th shows a distinct dependence on spatial dimension (d) and system size.
- In dimensions d>1, t_Th is finite and determined by intersite coupling.
- In one dimension, t_Th diverges with system size, creating a window where spectral correlations deviate from RMT.
Conclusions:
- The spatial dimension critically governs the emergence of RMT-like spectral statistics.
- A many-body localization transition was observed in the Floquet model.
- The spectral form factor's behavior in the localized phase was discussed.
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