Quantum phase transitions and commensurability in frustrated Josephson junction arrays

The superconductor-insulator transition of an array of Josephson junctions is studied. In junctions with small capacitance the interaction of charges introduces quantum fluctuations and shifts the phase transition. An external voltage controls the total charge and creates "charge frustration". Commensurability effects lead to similar structure in the phase diagram as had been found for magnetic frustration. The model used to describe a nonclassical junction array is similar to a Bose-Hubbard model. We study and compare the phase diagrams obtained from both models. If the interaction in the Bose model has a finite range we predict the commensurability to lead to a richly structured dependence on the chemical potential.