Quantum effects on the BKT phase transition of two-dimensional Josephson arrays

The phase diagram of two-dimensional Josephson arrays is studied by means of the mapping to the quantum XY model. The quantum effects on the thermodynamics of the system can be evaluated with quantitative accuracy by a semiclassical method, the pure-quantum self-consistent harmonic approximation, and those of dissipation can be included in the same framework by the Caldeira-Leggett model. Within this scheme, the critical temperature of the superconductor-metal transition, which is a Berezinskii-Kosterlitz-Thouless one, can be calculated in an extremely easy way as a function of the quantum coupling and of the dissipation mechanism. Previous quantum Monte Carlo results for the same model appear to be rather inaccurate, while a comparison with experimental data leads us to conclude that the commonly assumed dissipation model is not suitable to describe in detail a real system.