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arXiv:1205.2890 · Journal of Physics A Mathematical and Theoretical

Minimal models for a superconductor-insulator conformal quantum phase transition

M Cristina Diamantini, Carlo A. Trugenberger

Published Feb 27, 2013• 0 citations
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Abstract

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.

DOI
10.1088/1751-8113/46/11/115003

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A one-dimensional quantum version of the frustrated XY (planar rotor) model is considered which can be physically realized as a ladder of Josephson junctions at half a flux quantum per plaquette. This system undergoes a superconductor to insulator transition at zero temperature as a function of charging energy. The critical behavior is studied using a Monte Carlo transfer matrix applied to the path-integral representation of the model and a finite-size-scaling analysis of data on small system sizes. Depending on the ratio between the interchain and intrachain couplings the system can have single or double transitions which is consistent with the prediction that its critical behavior should be described by the two-dimensional classical XY-Ising model.
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We study the superconductor-insulator transition of a two-dimensional Bose-Hubbard model, considering as a specific example, an array of Josephson junctions. Within a coarse-graining approach we derive an effective free-energy functional from which we determine the phase diagram. At zero temperature it consists of a superconducting phase and Mott-insulating lobes. The phase boundaries of some of these lobes display reentrant behavior as a function of temperature. Next, we evaluate the electromagnetic-response functions of the system. The real part of the longitudinal conductivity is characterized by an excitation gap, whereas the imaginary part describes a capacitor. In an ideal system, under certain conditions a universal conductance is found at the transition. If we add low-frequency dissipation to the model a different value of the universal conductance is found, but still it is independent of the strength of the dissipation. Qualitatively differing results are obtained for frustrated and unfrustrated systems. We also discuss the Hall conductance of the system.