Mean-field theories for the quantum phase transition in Josephson junction arrays

Abstract

We compare two different approaches which both attempt to describe the zero-temperature superconductor-insulator transition in Josephson junction arrays through an effective Ginzburg-Landau functional. Both methods agree only for the special case of a diagonal capacitance matrix (self-charging limit). While the differences in the phase diagram are less significant, we find that the phase diagram are less significant, we find that the fourth order term of the “coarse-grained” functional changes its sign when the range of the interaction, λ, exceeds a few lattice constants. On the other hand, a variational ansatz predicts a positive sign with a coefficient which increases with increasing λ, which implies a large critical region and strong correlation between order parameter fluctuations.