  The phase diagram of a 2D Josephson junction array with large substrate
resistance, described by a quantum XY model, is studied by means of Fourier
path-integral Monte Carlo. A genuine Berezinskii-Kosterlitz-Thouless transition
is found up to a threshold value g* of the quantum coupling, beyond which no
phase coherence is established. Slightly below g* the phase stiffness shows a
reentrant behavior with temperature, in connection with a low-temperature
disappearance of the superconducting phase, driven by strong nonlinear quantum
fluctuations.
