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arXiv · 1503.07974

How accurately can the microcanonical ensemble describe small isolated quantum systems?

Tatsuhiko N. Ikeda·Masahito Ueda
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Abstract

We numerically investigate quantum quenches of a nonintegrable hard-core Bose-Hubbard model to test the accuracy of the microcanonical ensemble in small isolated quantum systems. We show that, in a certain range of system size, the accuracy increases with the dimension of the Hilbert space $D$ as $1/D$. We ascribe this rapid improvement to the absence of correlations between many-body energy eigenstates as well as to the eigenstate thermalization. Outside of that range, the accuracy is found to scale as $1/\sqrt{D}$ and improves algebraically with the system size.

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Tatsuhiko N. Ikeda, Masahito Ueda. 2015-03-27. How accurately can the microcanonical ensemble describe small isolated quantum systems?. https://doi.org/10.1103/physreve.92.020102

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