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-c(0){1+c(1)an(1/3)+[c(2)(') ln(an(1/3))+c(2)(')]a(2)n(2/3)+O(a(3)n)}, where T-c(0) 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 , Phys. Rev. Lett. 79, 3549 (1997)] in order to understand the difference in the value of the coefficient c(1) between their results and the (apparently) other reliable results in the literature. Our results show that {(T-c-T-c(0))/T-c(0)}/(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 c(1)=1.32+/-0.14, in agreement with results from recent Monte Carlo methods of three-dimensional O(2) scalar phi(4) field theory and variational perturbation theory.