Minimal models for a superconductor-insulator conformal quantum phase transition

Conformal field theories do not only classify two dimensional (2D) classical critical behaviour, but they also govern a certain class of 2D quantum critical behaviour. In this latter case, it is the ground state wave functional of the quantum theory that is conformally invariant, rather than the classical action. We show that the superconducting-insulating (SI) quantum phase transition in 2D Josephson junction arrays (JJAs) is a (doubled) c = 1 Gaussian conformal quantum critical point. The quantum action describing this system is a doubled Maxwell-Chern-Simons model in the strong coupling limit. We also argue that the SI quantum transitions in frustrated JJAs realize the other possible universality classes of conformal quantum critical behaviour, corresponding to the unitary minimal models at central charge c = 1 - 6/m(m + 1) for m ⩾ 3.