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

Rapid Communication

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

Tatsuhiko N. Ikeda and Masahito Ueda

Phys. Rev. E 92, 020102(R) – Published 5 August 2015

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. Outside of that range, the accuracy is found to scale either as $1 / \sqrt{D}$ or algebraically with the system size.