Application of machine learning in Bose-Einstein condensation critical-temperature analyses of path-integral Monte Carlo simulations

TL;DR

This paper demonstrates how simple machine learning algorithms can accurately determine the critical temperature of Bose-Einstein condensation from path-integral Monte Carlo simulation data, offering a new approach to analyzing quantum phase transitions.

Contribution

It introduces a machine learning-based method for critical temperature analysis in Bose-Einstein condensation, comparing favorably with existing techniques.

Findings

Machine learning methods agree well with traditional analysis techniques.

The approach is applied to Coulomb Bose gases and liquid helium-4.

Results show efficient and accurate critical temperature determination.

Abstract

We detail the use of simple machine learning algorithms to determine the critical Bose-Einstein condensation (BEC) critical temperature $T_\text{c}$ from ensembles of paths created by path-integral Monte Carlo (PIMC) simulations. We quickly overview critical temperature analysis methods from literature, and then compare the results of simple machine learning algorithm analyses with these prior-published methods for one-component Coulomb Bose gases and liquid $^4$He, showing good agreement.