Spectral Statistics in Spatially Extended Chaotic Quantum Many-Body Systems

We study spectral statistics in spatially extended chaotic quantum many-body systems, using simple lattice Floquet models without time-reversal symmetry. Computing the spectral form factor K(t) analytically and numerically, we show that it follows random matrix theory (RMT) at times longer than a ma...

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Bibliographic Details
Published in:Physical review letters 2018-08, Vol.121 (6), p.060601-060601, Article 060601
Main Authors: Chan, Amos, De Luca, Andrea, Chalker, J T
Format: Article
Language:English
Subjects:
Computing time
Dependence
Form factors
Many body interactions
Mathematical models
Matrix theory
Spectra
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Summary:We study spectral statistics in spatially extended chaotic quantum many-body systems, using simple lattice Floquet models without time-reversal symmetry. Computing the spectral form factor K(t) analytically and numerically, we show that it follows random matrix theory (RMT) at times longer than a many-body Thouless time, t_{Th}. We obtain a striking dependence of t_{Th} on the spatial dimension d and size of the system. For d>1, t_{Th} is finite in the thermodynamic limit and set by the intersite coupling strength. By contrast, in one dimension t_{Th} diverges with system size, and for large systems there is a wide window in which spectral correlations are not of RMT form. Lastly, our Floquet model exhibits a many-body localization transition, and we discuss the behavior of the spectral form factor in the localized phase.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.121.060601