We present precise path-integral Monte Carlo results for the thermodynamics of a homogeneous dilute Bose gas. Pressure and energy are calculated as a function of temperature both below and above the Bose-Einstein transition. Specifically, we address interaction effects, focusing on deviations from the ideal-gas law in the thermodynamic limit. We also calculate the isothermal compressibility and the contact parameter, which provide a clear signature of the role played by interactions. In particular, we obtain indications of a discontinuity of the compressibility at the transition point. To gain physical insight, numerical results are systematically compared with the predictions of first-order Hartree-Fock and second-order Popov theories, both giving an approximate description of the gas thermodynamics. The comparison shows the extension of the critical region around the transition point, where the inaccuracies of the perturbative expansions are more pronounced.
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
as of the Bose-Hubbard model is
as/al=0.316(2) where
al is the lattice constant. It turned out that inclusion of the universal second correction term of
O(nlogn) makes the fitting worse while it is restored by inclusion of the non-universal third correction term, of which the existence was predicted analytically.
By using exact path-integral Monte Carlo methods we calculate the equation of state of an interacting Bose gas as a function of temperature both below and above the superfluid transition. The universal character of the equation of state for dilute systems and low temperatures is investigated by modeling the interatomic interactions using different repulsive potentials corresponding to the same
s-wave scattering length. The results obtained for the energy and the pressure are compared to the virial expansion for temperatures larger than the critical temperature. At very low temperatures we find agreement with the ground-state energy calculated using the diffusion Monte Carlo method.
Using a finite-temperature path integral Monte Carlo simulation (PIMC) method and finite-size scaling, we have investigated the interaction-induced shift of the phase-transition temperature for Bose-Einstein condensation of homogeneous weakly interacting Bose gases in three dimensions, which is given by a proposed analytical expression ${T}_{c}={T}_{c}^{0}{1+{c}_{1}a{n}^{1∕3}+[{c}_{2}^{\ensuremath{'}}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}(a{n}^{1∕3})+{c}_{2}^{\ensuremath{''}}]{a}^{2}{n}^{2∕3}+\mathrm{O}({a}^{3}n)}$, where
Tc0 is the critical temperature for an ideal gas,
a is the
s-wave scattering length, and
n is the number density. We have used smaller number densities and more time slices than in the previous PIMC simulations [Gruter et al., Phys. Rev. Lett. 79, 3549 (1997)] in order to understand the difference in the value of the coefficient
c1 between their results and the (apparently) other reliable results in the literature. Our results show that ${({T}_{c}\ensuremath{-}{T}_{c}^{0})∕{T}_{c}^{0}}∕(a{n}^{1∕3})$ depends strongly on the interaction strength
an1∕3 while the previous PIMC results are considerably flatter and smaller than our results. We obtain ${c}_{1}=1.32\ifmmode\pm\else\textpm\fi{}0.14$, in agreement with results from recent Monte Carlo methods of three-dimensional O(2) scalar ${\ensuremath{\phi}}^{4}$ field theory and variational perturbation theory.