CRITICAL PROPERTIES OF 2-DIMENSIONAL JOSEPHSON-JUNCTION ARRAYS WITH ZERO-POINT QUANTUM FLUCTUATIONS

We present results from an extensive analytic and numerical study of a two-dimensional model of a square array of ultrasmall Josephson junct ions. We include the ultrasmall self-capacitance and mutual capacitanc e of the junctions, for the same parameter ranges as those produced in the experiments. The model Hamiltonian studied includes the Josephson , E(J), as well as the charging, E(C), energies between superconductin g islands. The corresponding quantum partition function is expressed i n different calculationally convenient ways within its path-integral r epresentation. The phase diagram is analytically studied using a WKB r enormalization group (WKB-RG) plus a self-consistent harmonic approxim ation (SCHA) analysis, together with nonperturbative quantum Monte Car lo (QMC) simulations. Most of the results presented here pertain to th e superconductor to normal (S-N) region, although some results for the insulating to normal (I-N) region are also included. We find very goo d agreement between the WKB-RG and QMC results when compared to the ex perimental data. To fit the data, we only used the experimentally dete rmined capacitances as fitting parameters. The WKB-RG analysis in the S-N region predicts a low-temperature instability, i.e., a quantum-ind uced transition (QUIT). We carefully analyze the possible existence of the QUIT via the QMC simulations and carry out a finite-size analysis of T-QUIT as a function of the magnitude of the imaginary-time axis L (tau). We find that for some relatively large values of alpha = E(C)/E (J) (1 less than or equal to alpha less than or equal to 2.25), the L( tau)-->infinity limit does appear to give a nonzero T-QUIT, while for alpha less than or equal to 2.5, T-QUIT = 0. We use the SCHA to analyt ically understand the L(tau) dependence of the QMC results with good a greement between them. Finally, we also carried out a WKB-RG analysis in the I-N region and found no evidence of a low-temperature QUIT, up to lowest order in alpha(-1).