Conductivity near the Superconductor-Insulator Transition of a 2-Dimensional Bose-Hubbard System

We study the superconductor-insulator transition of a 2-dimensional Bose-Hubbard model, considering as a physical realization an array of Josephson junctions. Within a coarse-graining approach we derive an effective free energy functional, from which we determine the phase-boundary. It also allows us to calculate the electromagnetic response as a function of temperature and system parameters, magnetic field, and chemical potential. The conductivity is characterized by an excitation gap in the real part, whereas the imaginary part behaves capacitively. Under special conditions a universal conductance appears at the transition. Qualitatively different results are obtained for frustrated and unfrustrated systems.