High-precision simulation of finite-size thermalizing systems at long times

TL;DR

The paper introduces an efficient numerical method to simulate thermalizing quantum systems at long times with higher-order finite-size error scaling, leveraging the eigenstate thermalization hypothesis.

Contribution

It proposes a novel numerical approach that reduces finite-size errors in simulating thermal properties of quantum systems, assuming the eigenstate thermalization hypothesis.

Findings

Error scaling is improved to higher order in 1/N.

Method is validated under the eigenstate thermalization hypothesis.

Simulation accuracy increases for larger system sizes.

Abstract

To simulate thermalizing systems at long times, the most straightforward approach is to calculate the thermal properties at the corresponding energy. In a quantum many-body system of size $N$, for local observables and many initial states, this approach has an error of $O(1/N)$, which is reminiscent of the finite-size error of the equivalence of ensembles. In this paper, we propose a simple and efficient numerical method so that the simulation error is of higher order in $1/N$. This finite-size error scaling is proved by assuming the eigenstate thermalization hypothesis.