Critical parameters from trap-size scaling in trapped particle systems

TL;DR

This paper uses quantum Monte Carlo simulations to analyze the critical behavior of trapped Bose-Hubbard systems at the superfluid transition, providing a systematic method to determine critical parameters via trap-size scaling.

Contribution

It introduces a numerical scheme based on trap-size scaling to accurately extract critical parameters from trapped particle systems at phase transitions.

Findings

Critical parameters can be derived from trap-size dependence of observables.

The method converges to true critical parameters in the large trap-size limit.

Guides experimental determination of critical parameters in cold atom systems.

Abstract

We investigate the critical behavior of trapped particle systems at the low-temperature superfluid transition. In particular, we consider the three-dimensional Bose-Hubbard model in the presence of a trapping harmonic potential coupled with the particle density, which is a realistic model of cold bosonic atoms in optical lattices. We present a numerical study based on quantum Monte Carlo simulations, analyzed in the framework of the trap-size scaling (TSS). We show how the critical parameters can be derived from the trap-size dependences of appropriate observables, matching them with TSS. This provides a systematic scheme which is supposed to exactly converge to the critical parameters of the transition in the large trap-size limit. Our numerical analysis may provide a guide for experimental investigations of trapped systems at finite-temperature and quantum transitions, showing how critical parameters may be determined by looking at the scaling of the critical modes with respect to the trap size, i.e. by matching the trap-size dependence of the experimental data with the expected TSS Ansatz.