Publication: Long-range level correlations in quantum systems with finite Hilbert space dimension
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2021-01-11
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American Physical Society
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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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©2021 American Physical Society. The authors thank R. A. Molina for his careful reading and useful suggestions. This work has been financially supported by Ministerio de Economía, Industria y Competitividad/Fondo Europeo de Desarrollo Regional (MINECO/FEDER) Grant No. FIS2015-63770-P and Ministerio de Ciencia, Innovación y Universidades/Agencia Estatal de Investigación (MCIU/AEI/FEDER) Grant No. PGC2018094180-B-I00.