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 $\mathrm{XY}$ 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.