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We provide an in depth analysis of the theory proposed by Holzmann,Chevallier and Krauth (HCK) [Europhys. Lett., {\bf 82}, 30001 (2008)] forpredicting the temperature at which the Berezinskii-Kosterlitz-Thouless (BKT)transition to a superfluid state occurs in the harmonically trappedquasi-two-dimensional (2D) Bose gas. Their theory is based on a meanfield modelof the system density and we show that the HCK predictions change appreciablywhen an improved meanfield theory and identification of the transition point isused. In this analysis we develop a consistent theory that provides a lowerbound for the BKT transition temperature in the trapped quasi-2D Bose gas.

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