Three distinct types of quantum phase transitions in a (2+1)-dimensional array of dissipative Josephson junctions

Abstract

We have performed large-scale Monte Carlo simulations on a model describing a (2+1)-dimensional array of dissipative Josephson junctions. We find three distinct stable quantum phases of the system. The most ordered state features long-range spatial ordering in the phase θ of the superconducting order parameter, but temporal ordering only in spatial gradients Δθ, not in θ. Significantly, the most ordered state therefore does not have three-dimensional (3D) XY ordering. Rather, it features two-dimensional (2D) spin waves coexisting with temporally disordered phases θ. There is also an intermediate phase featuring quasi-long-range spatial order in θ coexisting with a gas of instantons in Δθ. We briefly discuss possible experimental signatures of such a state, which may be viewed as a local metal and a global superconductor. The most disordered state has phase disorder in all spatio-temporal directions, and may be characterized as a gas of proliferated vortices coexisting with a gas of Δθ instantons. The phase transitions between these phases are discussed. The transition from the most ordered state to the intermediate state is driven by proliferation of instantons in Δθ. The transition from the intermediate state to the most disordered state is driven by the proliferation of spatial point vortices in the background of a proliferated Δθ-instanton gas, and constitutes a Berezinskii-Kosterlitz-Thouless phase transition. The model also features a direct phase transition from the most ordered state to the most disordered state, and this transition is neither in the 2D XY nor in the 3D XY universality class. It comes about via a simultaneous proliferation of point vortices in two spatial dimensions and Δθ instantons, with a complicated interplay between them. The results are compared to, and differ in a fundamental way from, the results that are found in dissipative quantum rotor systems. The difference originates with the difference in the values that the fundamental degrees of freedom can take in the latter systems compared to dissipative Josephson junction arrays.

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