%0 Journal Article
%A Corps, Angel L.
%A Relaño Pérez, Armando
%T Long-range level correlations in quantum systems with finite Hilbert space dimension
%D 2021
%@ 2470-0045
%U https://hdl.handle.net/20.500.14352/8271
%X We study the spectral statistics of quantum systems with finite Hilbert spaces. We derive a theorem showing that eigenlevels in such systems cannot be globally uncorrelated, even in the case of fully integrable dynamics, as a consequence of the unfolding procedure. We provide an analytic expression for the power spectrum of the delta(n) statistic for a model of intermediate statistics with level repulsion but independent spacings, and we show both numerically and analytically that the result is spoiled by the unfolding procedure. Then, we provide a simple model to account for this phenomenon, and test it by means of numerics on the disordered XXZ chain, the paradigmatic model of many-body localization, and the rational Gaudin-Richardson model, a prototypical model for quantum integrability.
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