Long-range level correlations in quantum systems with finite Hilbert space dimension

• URL: http://arxiv.org/abs/2010.06489v2
• Date: Wed, 13 Jan 2021 09:34:52 GMT
• Title: Long-range level correlations in quantum systems with finite Hilbert space dimension
• Authors: \'Angel L. Corps, Armando Rela\~no
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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