Spectral statistics in spatially extended chaotic quantum many-body systems

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

5 pages, 5 figures. To appear in PRL

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