Truncation error in series expansions linking microcanonical and canonical ensembles

TL;DR

This paper analyzes the truncation error in series expansions linking microcanonical and canonical ensembles, showing exponential decay under certain conditions and providing guidelines for parameter setting.

Contribution

It proves the exponential decay of truncation error in the mTPQ method when the effective temperature is below the target temperature, and discusses parameter optimization.

Findings

Truncation error decreases exponentially with system size under specific conditions.

Error remains constant if the effective temperature exceeds the target temperature.

Guidelines for setting mTPQ parameters to balance error and computational cost.

Abstract

In the microcanonical thermal pure quantum (mTPQ) method, the canonical ensemble is derived using Taylor series expansions. We prove that the truncation error decreases exponentially with system size when the effective temperature of the mTPQ state is smaller than the target temperature, and otherwise, the error remains constant. We also show the discipline to set the mTPQ parameter by considering the trade-off between the error and the numerical cost.