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arXiv · 1803.03841

Spectral statistics in spatially extended chaotic quantum many-body systems

Amos Chan·Andrea De Luca·J. T. Chalker
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Abstract

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, $t_{\rm Th}$. We obtain a striking dependence of $t_{\rm Th}$ on the spatial dimension $d$ and size of the system. For $d>1$, $t_{\rm Th}$ is finite in the thermodynamic limit and set by the inter-site coupling strength. By contrast, in one dimension $t_{\rm Th}$ diverges with system size, and for large systems there is a wide window in which spectral correlations are not of RMT form.

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Amos Chan, Andrea De Luca, J. T. Chalker. 2018-08-03. Spectral statistics in spatially extended chaotic quantum many-body systems. https://doi.org/10.1103/physrevlett.121.060601

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