Bose-Einstein Condensation Temperature of a Homogeneous Weakly Interacting Bose Gas : PIMC study

Abstract

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 $T_c=T_c^0\{1+c_{1}a{n}^{1/3}+[c_2^{\prime }\ln (a{n}^{1/3})+c_2^{\prime \prime }]a^2{n}^{2/3}+O(a^{3}n)\}$, 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 {\it et al.}, Phys. Rev. Lett. {\bf 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 $\{(T_c-T_c^0)/T_c^0\}/(a{n}^{1/3})$ depends strongly on the interaction strength $a{n}^{1/3}$ while the previous PIMC results are considerably flatter and smaller than our results. We obtain $c_1$ = 1.32 $\pm$ 0.14, in agreement with results from recent Monte Carlo methods of three-dimensional O(2) scalar ${\varphi }^4$ field theory and variational perturbation theory.

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