The Fractional Quantum Hall effect in an array of quantum wires

We demonstrate the emergence of the quantum Hall (QH) hierarchy in a 2D model of coupled quantum wires in a perpendicular magnetic field. At commensurate values of the magnetic field, the system can develop instabilities to appropriate inter-wire electron hopping processes that drive the system into a variety of QH states. Some of the QH states are not included in the Haldane-Halperin hierarchy. In addition, we find operators allowed at any field that lead to novel crystals of Laughlin quasiparticles. We demonstrate that any QH state is the groundstate of a Hamiltonian that we explicitly construct.Comment: Revtex, 4 pages, 2 figure

Families of Graphs With Chromatic Zeros Lying on Circles

We define an infinite set of families of graphs, which we call $p$-wheels and denote $(Wh)^{(p)}_n$, that generalize the wheel ($p=1$) and biwheel ($p=2$) graphs. The chromatic polynomial for $(Wh)^{(p)}_n$ is calculated, and remarkably simple properties of the chromatic zeros are found: (i) the real zeros occur at $q=0,1,...p+1$ for $n-p$ even and $q=0,1,...p+2$ for $n-p$ odd; and (ii) the complex zeros all lie, equally spaced, on the unit circle $|q-(p+1)|=1$ in the complex $q$ plane. In the $n \to \infty$ limit, the zeros on this circle merge to form a boundary curve separating two regions where the limiting function $W(\{(Wh)^{(p)}\},q)$ is analytic, viz., the exterior and interior of the above circle. Connections with statistical mechanics are noted.Comment: 8 pages, Late

Charge order, superconductivity, and a global phase diagram of doped antiferromagnets

We investigate the interplay between lattice-symmetry breaking and superconducting order in a two-dimensional model of doped antiferromagnets, with long-range Coulomb interactions and Sp(2N) spin symmetry, in the large-N limit. Our results motivate the outline of a global phase diagram for the cuprate superconductors. We describe the quantum transitions between the phases, the evolution of their fermion excitation spectrum, and the experimental implications.Comment: 4 pages, 4 figs, final version as publishe

Thermal metal in network models of a disordered two-dimensional superconductor

We study the universality class for localization which arises from models of non-interacting quasiparticles in disordered superconductors that have neither time-reversal nor spin-rotation symmetries. Two-dimensional systems in this category, which is known as class D, can display phases with three different types of quasiparticle dynamics: metallic, localized, or with a quantized (thermal) Hall conductance. Correspondingly, they can show a variety of delocalization transitions. We illustrate this behavior by investigating numerically the phase diagrams of network models with the appropriate symmetry, and for the first time show the appearance of the metallic phase.Comment: 5 pages, 3 figure

Spin-Peierls states of quantum antiferromagnets on the CaV4O9Ca V_4 O_9 lattice

We discuss the quantum paramagnetic phases of Heisenberg antiferromagnets on the 1/5-depleted square lattice found in $Ca V_4 O_9$. The possible phases of the quantum dimer model on this lattice are obtained by a mapping to a quantum-mechanical height model. In addition to the ``decoupled'' phases found earlier, we find a possible intermediate spin-Peierls phase with spontaneously-broken lattice symmetry. Experimental signatures of the different quantum paramagnetic phases are discussed.Comment: 9 pages; 2 eps figure

A Local Moment Approach to magnetic impurities in gapless Fermi systems

A local moment approach is developed for the single-particle excitations of a symmetric Anderson impurity model (AIM), with a soft-gap hybridization vanishing at the Fermi level with a power law r > 0. Local moments are introduced explicitly from the outset, and a two-self-energy description is employed in which the single-particle excitations are coupled dynamically to low-energy transverse spin fluctuations. The resultant theory is applicable on all energy scales, and captures both the spin-fluctuation regime of strong coupling (large-U), as well as the weak coupling regime. While the primary emphasis is on single particle dynamics, the quantum phase transition between strong coupling (SC) and (LM) phases can also be addressed directly; for the spin-fluctuation regime in particular a number of asymptotically exact results are thereby obtained. Results for both single-particle spectra and SC/LM phase boundaries are found to agree well with recent numerical renormalization group (NRG) studies. A number of further testable predictions are made; in particular, for r < 1/2, spectra characteristic of the SC state are predicted to exhibit an r-dependent universal scaling form as the SC/LM phase boundary is approached and the Kondo scale vanishes. Results for the `normal' r = 0 AIM are moreover recovered smoothly from the limit r -> 0, where the resultant description of single-particle dynamics includes recovery of Doniach-Sunjic tails in the Kondo resonance, as well as characteristic low-energy Fermi liquid behaviour.Comment: 52 pages, 19 figures, submitted to Journal of Physics: Condensed Matte

Andreev tunnelling in quantum dots: A slave-boson approach

We study a strongly interacting quantum dot connected to a normal and to a superconducting lead. By means of the slave-boson technique we investigate the low temperature regime and discuss electrical transport through the dot. We find that the zero bias anomaly in the current-voltage characteristics which is associated to the occurance of the Kondo resonance in the quantum dot, is enhanced in the presence of superconductivity, due to resonant Andreev scattering.Comment: 4 pages, 1 figur

Chiral Dynamics and Fermion Mass Generation in Three Dimensional Gauge Theory

We examine the possibility of fermion mass generation in 2+1- dimensional gauge theory from the current algebra point of view.In our approach the critical behavior is governed by the fluctuations of pions which are the Goldstone bosons for chiral symmetry breaking. Our analysis supports the existence of an upper critical number of Fermion flavors and exhibits the explicit form of the gap equation as well as the form of the critical exponent for the inverse correlation lenght of the order parameterComment: Latex,10 pages,DFUPG 70/9

‘‘Lozenge’’ contour plots in scattering from polymer networks

We present a consistent explanation for the appearance of “lozenge” shapes in contour plots of the two dimensional scattering intensity from stretched polymer networks. By explicitly averaging over quenched variables in a tube model, we show that lozenge patterns arise as a result of chain material that is not directly deformed by the stretch. We obtain excellent agreement with experimental data

Nonlinear Dynamics of Composite Fermions in Nanostructures

We outline a theory describing the quasi-classical dynamics of composite fermions in the fractional quantum Hall regime in the potentials of arbitrary nanostructures. By an appropriate parametrization of time we show that their trajectories are independent of their mass and dispersion. This allows to study the dynamics in terms of an effective Hamiltonian although the actual dispersion is as yet unknown. The applicability of the theory is verified in the case of antidot arrays where it explains details of magnetoresistance measurements and thus confirms the existence of these quasiparticles.Comment: submitted to Europhys. Lett., 4 pages, postscrip