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

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.