Reentrant Behavior of the Phase Stiffness in Josephson Junction Arrays

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 $g^{\star }$ of the quantum coupling, beyond which no phase coherence is established. Slightly below $g^{\star }$ 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.