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

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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