We investigate the properties of strongly interacting bosons in two dimensions at zero temperature using mean-field theory, a variational Ansatz for the ground state wave function, and Monte Carlo methods. With on-site and short-range interactions a rich phase diagram is obtained. Apart from the homogeneous superfluid and Mott-insulating phases, inhomogeneous chargedensity wave phases appear, that are stabilized by the finite-range interaction.Furthermore, our analysis demonstrates the existence of a supersolid phase, in which both long-range order (related to the charge-density wave) and offdiagonal long-range order coexist. We also obtain the critical exponents for the various phase transitions.
We study the superconductor-insulator transition of a 2-dimensional Bose-Hubbard model, considering as a speci c example, an array of Josephson junctions. Within a coarse-graining approach w e derive an e ective free-energy functional from which w e 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 behaviour as a function of temperature. Next, we e v aluate the electromagnetic response functions of the system. The real part of the longitudinal conductivity i s c haracterized 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 di erent v alue of the universal conductance is found, but still it is independent of the strength of the dissipation. Qualitatively di ering results are obtained for frustrated and unfrustrated systems. We also discuss the Hall conductance of the system. PACS numbers: 72.20.-i 74.65.+n
We study transport properties of thin films near the superconductor-insulator transition. Formulated in a phase representation, the key new feature of our model is the assumption of a local Ohmic dissipative mechanism. Coarse graining leads to a Ginzburg-Landau description, with non-Ohmic dynamics for the order parameter. For strong enough damping a new universality class is found. It is characterized by a nonuniversal dc conductivity, and a damping-dependent dynamical critical exponent. The formulation also provides a description of the magnetic-field-tuned transition. Several microscopic mechanisms are proposed as the origin of the dissipation. [S0031-9007 (97)02541-6] PACS numbers: 74.76. -w, 74.50.+r
We study the influence of a tunable dissipative environment on the dynamics of Josephson junction arrays near the superconductor-insulator transition. The experimental realization of the environment is a two dimensional electron gas coupled capacitively to the array. This setup allows for the well controlled tuning of the dissipation by changing the resistance of the two dimensional electron gas. The capacitive coupling cuts off the dissipation at low frequencies. We determine the phase diagram and calculate the temperature and dissipation dependence of the array conductivity. We find good agreement with recent experimental results. [S0031-9007 (97)04157-4] PACS numbers: 74.50. + r, 74.25.Fy Quantum phase transitions attract intense attention because of their paradigmatic nature: they are relevant to a host of experimental issues. Examples include the superconductor-insulator (SI) transition in granular superconductors [1], the transition between quantum hall states [2], transitions in disordered magnets [3], and the physics of vortices in the presence of columnar disorder [4]. Josephson junction arrays constitute a particularly attractive testing ground for the SI transition, because all parameters are well under control, and are widely tunable [5,6]. In these systems the SI transition can be driven by quantum fluctuations when the charging energy E C becomes comparable to the Josephson coupling energy E J [7]. It was understood early that dissipation is also capable of driving an SI transition. The phase diagram of a single Josephson junction in a dissipative environment was explored by Schmid [8]. Strong dissipation suppresses quantum fluctuations and restores the classical behavior with a finite supercurrent. For weak damping, however, quantum fluctuations suppress the supercurrent to zero. When an array is built from the junctions, at strong dissipation phase fluctuations are again damped, favoring phase coherence and global superconductivity. This type of SI transition is present in arrays of Josephson junctions as well as in thin films [9][10][11][12].The experimental verification of a dissipation-tuned SI transition is still open. The actual strength of the dissipation is hard to control. An indicator may be the normal state resistance, although it is unclear how this translates into a dissipation below the bulk transition temperature, where the opening of a gap freezes out the gapless excitations [13]. It is also unsettled whether the dissipation or the Coulomb interaction is the main driving force for the transition. Recently the Berkeley group succeeded to fabricate and investigate Josephson junction arrays with tunable dissipation by placing an array on top of a two dimensional electron gas (2DEG), separated by an insulator [6]. The electron density and sheet resistance of the 2DEG are varied by tuning a gate voltage, without influencing the other parameters of the array. The main result is that the array resistance exhibits a temperature dependence, parametrized by the dissipation, which is reminisce...
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