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arXiv:cond-mat/0501219 · Physical Review B

Nature and boundary of the floating phase in a dissipative Josephson junction array

Sumanta Tewari, John Toner, Sudip Chakravarty

Published Feb 6, 2006• 17 citations
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Abstract

We study the nature of correlations within, and the transition into, the floating phase of dissipative Josephson junction arrays. Order parameter correlations in this phase are long-ranged in time, but only short-ranged in space. A perturbative renormalization group analysis shows that, in arbitrary spatial dimension, the transition is controlled by a continuous locus of critical fixed points determined entirely by the local topology of the lattice. This may be the most natural example of a line of critical points existing in arbitrary dimensions.

DOI
10.1103/physrevb.73.064503

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We study the nature of correlations within, and the transition into, the floating phase of dissipative Josephson junction arrays. Order parameter correlations in this phase are long-ranged in time, but only short-ranged in space. A perturbative renormalization group analysis shows that, in arbitrary spatial dimension, the transition is controlled by a continuous locus of critical fixed points determined entirely by the local topology of the lattice. This may be the most natural example of a line of critical points existing in arbitrary dimensions.
We show that dissipative Josephson junction arrays, an extended system, have an unusual ``floating'' metal phase in which the states of local (0+1)(0+1)(0+1)-dimensional elements (single junctions) can slide past each other despite arbitrary range spatial couplings among them. The zero-temperature metal-to-superconductor quantum phase transition is controlled in any dimension by a locus of critical points fixed only by the local lattice topology. Our theory can be tested by measuring $I\text{\ensuremath{-}}V$ characteristics. This may be the simplest and most natural example of a floating phase.
We study the T=0 normal to superconducting transition of Josephson arrays with {\it on-site} dissipation. A perturbative renormalization group solution is given. Like the previously studied case of {\it bond} dissipation (BD), this is a "floating" to coupled (FC) phase transition. {\it Unlike} the BD transition, at which {\it only} nearest-neighbor couplings become relevant, here {\it all} inter-grain couplings, out to {\it infinitely} large distances, do so simultaneously. We predict, for the first time in an FC transition, a diverging spatial correlation length. Our results show the robustness of floating phases in dissipative quantum systems.
Motivated by experiments on spin chains embedded in a metallic bath, as well as closed quantum systems described by long-range interacting Hamiltonians, we study a critical SU(N)\mathrm{SU}(N)SU(N) spin chain perturbed by dissipation, or equivalently, after space-time rotation, long-range spatial interactions. The interplay of dissipation and the Wess-Zumino (Berry phase) term results in a rich phase diagram with multiple renormalization-group fixed points. For a range of the exponent that characterizes the dissipative bath, we find a second-order phase transition between the fixed point that describes an isolated critical spin chain and a dissipation-induced-ordered phase. More interestingly, for a different range of the exponent, we find a stable, gapless, nonrelativistic phase of matter whose existence necessarily requires coupling to the dissipative bath. Upon tuning the exponent, we find that the fixed point corresponding to this gapless, stable phase ``annihilates'' the fixed point that describes the transition out of this phase to the ordered phase. We also study a relativistic version of our model, and we identify a new critical point. We discuss the implications of our work for Kondo lattice systems and engineered long-range interacting quantum systems.
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 $\ensuremath{\theta}$ of the superconducting order parameter, but temporal ordering only in spatial gradients $\ensuremath{\Delta}\ensuremath{\theta}$, not in $\ensuremath{\theta}$. Significantly, the most ordered state therefore does not have three-dimensional (3D) XYXYXY ordering. Rather, it features two-dimensional (2D) spin waves coexisting with temporally disordered phases $\ensuremath{\theta}$. There is also an intermediate phase featuring quasi-long-range spatial order in $\ensuremath{\theta}$ coexisting with a gas of instantons in $\ensuremath{\Delta}\ensuremath{\theta}$. 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 $\ensuremath{\Delta}\ensuremath{\theta}$ 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 $\ensuremath{\Delta}\ensuremath{\theta}$. 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 $\ensuremath{\Delta}\ensuremath{\theta}$-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 XYXYXY nor in the 3D XYXYXY universality class. It comes about via a simultaneous proliferation of point vortices in two spatial dimensions and $\ensuremath{\Delta}\ensuremath{\theta}$ 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.
We investigate the phase diagram of a one-dimensional dissipative Bose-Hubbard model using the nonperturbative functional renormalization group (FRG). Each lattice site is coupled to an independent bath, generating long-range temporal interactions that encode non-Markovian dissipation. For a broad class of bath spectra - ohmic, sub-ohmic, and super-ohmic - we identify two competing low-energy regimes: a Luttinger-liquid line of fixed points and a dissipative fixed point characterized by finite compressibility, vanishing superfluid stiffness, and universal scaling exponents, separated by a Berezinskii-Kosterlitz-Thouless transition. The FRG framework is essential here, as it provides access to the complete renormalization group flow and all fixed points from a single microscopic action, beyond the reach of perturbative or variational methods. This work establishes a unified and systematically improvable framework for describing dissipative quantum phases in one dimension.