The low-energy theory for the Bose-Hubbard model and the normal ground state of bosons

A bosonic realization of the SU(2) Lie algebra and of its vector representation is constructed, and an effective low-energy description of the Bose-Hubbard model in the form of anisotropic theory of quantum rotors is proposed and discussed. A possibility of a normal zero-temperature bosonic phase with neither crystalline nor superfluid order around the tip of the checkerboard-solid lobe at half-integer fillings is examined.Comment: 8 pages, LaTex, one postscript figur

New quantum phases in a one-dimensional Josephson array

We examine the phase diagram of an ordered one-dimensional Josephson array of small grains. The average grain charge in such a system can be tuned by means of gate voltage. At small grain-to-grain conductance, this system is strongly correlated because of the charge discreteness constraint (Coulomb blockade). At the gate voltages in the vicinity of the charge degeneracy points, we find new phases equivalent to a commensurate charge density wave and to a repulsive Luttinger liquid. The existence of these phases can be probed through a special dependence of the Josephson current on the gate voltage.Comment: 4 pages, including 1 eps figur

Quantum critical phenomena of long-range interacting bosons in a time-dependent random potential

We study the superfluid-insulator transition of a particle-hole symmetric system of long-range interacting bosons in a time-dependent random potential in two dimensions, using the momentum-shell renormalization-group method. We find a new stable fixed point with non-zero values of the parameters representing the short- and long-range interactions and disorder when the interaction is asymptotically logarithmic. This is contrasted to the non-random case with a logarithmic interaction, where the transition is argued to be first-order, and to the $1/r$ Coulomb interaction case, where either a first-order transition or an XY-like transition is possible depending on the parameters. We propose that our model may be relevant in studying the vortex liquid-vortex glass transition of interacting vortex lines in point-disordered type-II superconductors.Comment: 10 pages, 3 figure

The Field-Tuned Superconductor-Insulator Transition with and without Current Bias

The magnetic-field-tuned superconductor-insulator transition has been studied in ultrathin Beryllium films quench-condensed near 20 K. In the zero-current limit, a finite-size scaling analysis yields the scaling exponent product vz = 1.35 +/- 0.10 and a critical sheet resistance R_{c} of about 1.2R_{Q}, with R_{Q} = h/4e^{2}. However, in the presence of dc bias currents that are smaller than the zero-field critical currents, vz becomes 0.75 +/- 0.10. This new set of exponents suggests that the field-tuned transitions with and without dc bias currents belong to different universality classes.Comment: RevTex 4 pages, 4 figures, and 1 table minor change

Ground State and Excitations of Disordered Boson Systems

After an introduction to the dirty bosons problem, we present a gaussian theory for the ground state and excitations. This approach is physically equivalent to the Bogoliubov approximation. We find that ODLRO can be destroyed with sufficient disorder. The density of states and localization of the elementary excitations are discussed. (To appear in JLTP Proceedings of the Conference on Condensed Bose Systems at the University of Minnesota, 1993.)Comment: 13 pages. (postscript file because of the figures inserted in the text.

Anomalous Quantum Diffusion at the Superfluid-Insulator Transition

We consider the problem of the superconductor-insulator transition in the presence of disorder, assuming that the fermionic degrees of freedom can be ignored so that the problem reduces to one of Cooper pair localization. Weak disorder drives the critical behavior away from the pure critical point, initially towards a diffusive fixed point. We consider the effects of Coulomb interactions and quantum interference at this diffusive fixed point. Coulomb interactions enhance the conductivity, in contrast to the situation for fermions, essentially because the exchange interaction is opposite in sign. The interaction-driven enhancement of the conductivity is larger than the weak-localization suppression, so the system scales to a perfect conductor. Thus, it is a consistent possibility for the critical resistivity at the superconductor-insulator transition to be zero, but this value is only approached logarithmically. We determine the values of the critical exponents $\eta,z,\nu$ and comment on possible implications for the interpretation of experiments

Evidence of Vortices on the Insulating Side of the Superconductor-Insulator Transition

The magnetoresistance of ultrathin insulating films of Bi has been studied with magnetic fields applied parallel and perpendicular to the plane of the sample. Deep in the strongly localized regime, the magnetoresistance is negative and independent of field orientation. As film thicknesses increase, the magnetoresistance becomes positive, and a difference between values measured in perpendicular and parallel fields appears, which is a linear function of the magnetic field and is positive. This is not consistent with the quantum interference picture. We suggest that it is due to vortices present on the insulating side of the superconductor-insulator transition.Comment: 4 pages, 3 figure

Evolution of the Density of States Gap in a Disordered Superconductor

It has only recently been possible to study the superconducting state in the attractive Hubbard Hamiltonian via a direct observation of the formation of a gap in the density of states N(w). Here we determine the effect of random chemical potentials on N(w) and show that at weak coupling, disorder closes the gap concurrently with the destruction of superconductivity. At larger, but still intermediate coupling, a pseudo-gap in N(w) remains even well beyond the point at which off-diagonal long range order vanishes. This change in the elementary excitations of the insulating phase corresponds to a crossover between Fermi- and Bose-Insulators. These calculations represent the first computation of the density of states in a finite dimensional disordered fermion model via the Quantum Monte Carlo and maximum entropy methods.Comment: 4 pages, 4 figure

Phases of the one-dimensional Bose-Hubbard model

The zero-temperature phase diagram of the one-dimensional Bose-Hubbard model with nearest-neighbor interaction is investigated using the Density-Matrix Renormalization Group. Recently normal phases without long-range order have been conjectured between the charge density wave phase and the superfluid phase in one-dimensional bosonic systems without disorder. Our calculations demonstrate that there is no intermediate phase in the one-dimensional Bose-Hubbard model but a simultaneous vanishing of crystalline order and appearance of superfluid order. The complete phase diagrams with and without nearest-neighbor interaction are obtained. Both phase diagrams show reentrance from the superfluid phase to the insulator phase.Comment: Revised version, 4 pages, 5 figure

Effect of granularity on the insulator-superconductor transition in ultrathin Bi films

We have studied the insulator-superconductor transition (IST) by tuning the thickness in quench-condensed $Bi$ films. The resistive transitions of the superconducting films are smooth and can be considered to represent "homogeneous" films. The observation of an IST very close to the quantum resistance for pairs, $R_{\Box}^N \sim h/4e^2$ on several substrates supports this idea. The relevant length scales here are the localization length, and the coherence length. However, at the transition, the localization length is much higher than the superconducting coherence length, contrary to expectation for a "homogeneous" transition. This suggests the invalidity of a purely fermionic model for the transition. Furthermore, the current-voltage characteristics of the superconducting films are hysteretic, and show the films to be granular. The relevant energy scales here are the Josephson coupling energy and the charging energy. However, Josephson coupling energies ($E_J$) and the charging energies ($E_c$) at the IST, they are found to obey the relation $E_J < E_c$. This is again contrary to expectation, for the IST in a granular or inhomogeneous, system. Hence, a purely bosonic picture of the transition is also inconsistent with our observations. We conclude that the IST observed in our experiments may be either an intermediate case between the fermioinc and bosonic mechanisms, or in a regime of charge and vortex dynamics for which a quantitative analysis has not yet been done.Comment: accepted in Physical Review