Minimal Models for a Superconductor-Insulator Conformal Quantum Phase Transition

TL;DR

This paper demonstrates that the superconductor-insulator transition in 2D Josephson junction arrays is governed by a conformal quantum critical point described by a doubled Maxwell-Chern-Simons model, revealing new universality classes.

Contribution

It identifies the SI quantum phase transition as a conformal quantum critical point and introduces a doubled Maxwell-Chern-Simons model as its effective description.

Findings

SI transition is a doubled c=1 Gaussian conformal quantum critical point

Quantum action is a doubled Maxwell-Chern-Simons model in strong coupling

Frustrated JJAs realize other conformal universality classes at c=1-6/m(m+1)

Abstract

Conformal field theories do not only classify 2D classical critical behavior but they also govern a certain class of 2D quantum critical behavior. 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 behavior, corresponding to the unitary minimal models at central charge $c=1-6/m(m+1)$.