Universal and Non-Universal Correction Terms of Bose Gases in Dilute Region: a Quantum Monte Carlo Study

TL;DR

This study uses quantum Monte Carlo simulations to analyze correction terms in dilute Bose gases, revealing that non-universal third correction terms improve the fit over universal second correction terms.

Contribution

It provides the first detailed numerical validation of non-universal correction terms in the extended Lee-Huang-Yang formula for dilute Bose gases.

Findings

Inclusion of non-universal third correction term improves fitting accuracy.

Estimated s-wave scattering length ratio is a_s/a_l = 0.316(2).

Universal second correction term worsens fit, non-universal third correction restores it.

Abstract

We study dilute gases of interacting bosons at zero-temperature in the region where the system is characterized only by the s-wave scattering length. We carry out quantum Monte Carlo simulation of the Bose Hubbard model and a continuous-space hard-core model. Fitting the extended Lee-Huang-Yang formula to the Monte Carlo results establishes the detailed mapping from the lattice model to the continuous field theory characterized only by the s-wave scattering length. Our estimate of the intrinsic s-wave scattering length $a_s$ of the Bose-Hubbard model is $a_s/a_l = 0.316(2)$ where $a_l$ is the lattice constant. It turned out that inclusion of the universal second correction term of $O(n \log n)$ makes the fitting worse while it is restored by inclusion of the non-universal third correction term, of which the existence was predicted analytically.