Bose-Einstein condensation temperature of a homogeneous weakly interacting Bose gas: Path integral Monte Carlo study

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_c⁰{1+c₁an^1∕3+[c₂^′ ln(an^1∕3)+c₂^″]a²n^2∕3+O(a³n)}, where T_c⁰ 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−T_c⁰)∕T_c⁰}∕(an^1∕3) depends strongly on the interaction strength an^1∕3 while the previous PIMC results are considerably flatter and smaller than our results. We obtain c₁=1.32±0.14, in agreement with results from recent Monte Carlo methods of three-dimensional O(2) scalar ϕ⁴ field theory and variational perturbation theory.