  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.
