Analysis of the Holzmann-Chevallier-Krauth theory for the trapped quasi-two-dimensional Bose gas

We provide an in-depth analysis of the theory proposed by Holzmann, Chevallier, and Krauth (HCK) [Europhys. Lett. 82, 30001 (2008)] for predicting the temperature at which the Berezinskii-Kosterlitz-Thouless (BKT) transition to a superfluid state occurs in the harmonically trapped quasi-two-dimensional (2D) Bose gas. Their theory is based on a mean-field model of the system density, and we show that the HCK predictions change appreciably when an improved mean-field theory and identification of the transition point is used. In this analysis we develop a consistent theory that provides a lower bound for the BKT transition temperature in the trapped quasi-2D Bose gas.