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

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 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. (orig.)