Comment on ``Critical temperature of trapped hard-sphere Bose gases''

TL;DR

This paper critiques a recent Monte Carlo study on trapped hard-sphere Bose gases, highlighting a significant discretization error that affects the reported critical temperature results.

Contribution

It provides a critical analysis of the previous calculation, emphasizing the impact of discretization errors on the findings.

Findings

The original study's critical temperature remains unchanged by interactions.

The calculation has a serious discretization error affecting results.

The critique suggests the need for more accurate computational methods.

Abstract

In this comment, I discuss a recent path-integral Monte Carlo calculation by Pearson, Pang, and Chen (Phys. Rev. A 58, 4796 (1998)). For bosons with a small hard-core interaction in a harmonic trap, the authors find a critical temperature which does not change with respect to the non-interacting gas. The calculation suffers from a serious discretization error of the many-particle density matrix.