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{sub c}=T{sub c}{sup 0}{l_brace}1+c{sub 1}an{sup 1/3}+[c{sub 2}{sup '} ln(an{sup 1/3})+c{sub 2}]a{sup 2}n{sup 2/3}+O(a{sup 3}n){r_brace}, where T{sub c}{sup 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 et al., Phys. Rev. Lett. 79, 3549 (1997)] in order to understand the difference in the value of the coefficient c{sub 1} between their results and the (apparently) other reliable results in the literature. Our results show that {l_brace}(T{sub c}-T{sub c}{sup 0})/T{sub c}{sup 0}{r_brace}/(an{sup 1/3}) depends strongly on the interaction strength an{sup 1/3} while the previous PIMC results are considerably flatter and smaller than our results. We obtain c{sub 1}=1.32{+-}0.14, in agreement with results from recent Monte Carlo methods of three-dimensional O(2) scalar {phi}{sup 4} field theory and variational perturbation theory.