  By using a renormalization group analysis, we study the effect of
interparticle interactions on the critical temperature at which the
Berezinskii-Kosterlitz-Thouless (BKT) transition occurs for Bose-Einstein
condensates loaded at finite temperature in a 2D optical lattice. We find that
the critical temperature decreases as the interaction energy decreases; when
U/J=36/\pi one has a vanishing critical temperature, signaling the possibility
of a quantum phase transition of BKT type.
