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arXiv1995

Mean Field Description of the Fractional Quantum Hall Effect Near $ν=1/(2k+1)$

The nature of Mean Field Solutions to the Equations of Motion of the Chern--Simons Landau--Ginsberg (CSLG) description of the Fractional Quantum Hall Effect (FQHE) is studied. Beginning with the conventional description of this model at some chemical potential $μ_0$ and magnetic field $B$ corresponding to a ``special'' filling fraction $ν=2πρ/eB=1/n$ ($n=1,3,5\cdot \cdot\cdot$) we show that a deviation of $μ$ in a finite range around $μ_0$ does not change the Mean Field solution and thus the mean density of particles in the model. This result holds not only for the lowest energy Mean Field solution but for the vortex excitations as well. The vortex configurations do not depend on $μ$ in a finite range about $μ_0$ in this model. However when $μ-μ_0 < μ_{cr}^-$ (or $μ-μ_0>μ_{cr}^+$) the lowest energy Mean Field solution describes a condensate of vortices (or antivortices). We give numerical examples of vortex and antivortex configurations and discuss the range of $μ$ and $ν$ over which the system of vortices is dilute.

hep-th↗
arXiv1995

PHASE TRANSITION OF N-COMPONENT SUPERCONDUCTORS

We investigate the phase transition in the three-dimensional abelian Higgs model for N complex scalar fields, using the gauge-invariant average action Γ_{k}. The dependence of Γ_{k} on the effective infra-red cut-off k is described by a non-perturbative flow equation. The transition turns out to be first- or second-order, depending on the ratio between scalar and gauge coupling. We look at the fixed points of the theory for various N and compute the critical exponents of the model. Comparison with results from the ε-expansion shows a rather poor convergence for ε=1 even for large N. This is in contrast to the surprisingly good results of the ε-expansion for pure scalar theories. Our results suggest the existence of a parameter range with a second-order transition for all N, including the case of the superconductor phase transition for N=1.

cond-mat↗
arXiv1992

Hierarchical Wave Functions and Fractional Statistics in Fractional Quantum Hall Effect on the Torus

One kind of hierarchical wave functions of Fractional Quantum Hall Effect (FQHE) on the torus are constructed. The multi-component nature of anyon wave functions and the degeneracy of FQHE on the torus are very clear reflected in this kind of wave functions. We also calculate the braid statistics of the quasiparticles in FQHE on the torus and show they fit to the picture of anyons interacting with magnetic field on the torus obtained from braid group analysis.

cond-mat↗
arXiv1994

Mutifractal Analysis of Broadly Distributed Observables at Criticality

The multifractal analysis of disorder induced localization-delocalization transitions is reviewed. Scaling properties of this transition are generic for multi parameter coherent systems which show broadly distributed observables at criticality. The multifractal analysis of local measures is extended to more general observables including scaling variables such as the conductance in the localization problem. The relation of multifractal dimensions to critical exponents such as the order parameter exponent $β$ and the correlation length exponent $ν$ is investigated. We discuss a number of scaling relations between spectra of critical exponents, showing that all of the critical exponents necessary to characterize the critical phenomenon can be obtained within the generalized multifractal analysis. Furthermore we show how bounds for the correlation length exponent $ν$ are obtained by the typical order parameter exponent $α_0$ and make contact between the multifractal analysis and the finite size scaling approach in 2-d by relying on conformal mapping arguments.

cond-mat↗
arXiv1993

The Quartet State of the Two-Dimensional Heisenberg Model with Spin 1/2 on a Square Lattice

The low-energy properties of the two-dimensional Heisenberg model with spin-$\frac{1}{2}$ on a square lattice are investigated on the basis of the local dimer order. The lattice is divided into square blocks consisting of the quartet of spins. The spin variables and the Heisenberg Hamiltonian are expressed in terms of the low-energy quartet variables. On the basis of the Dyson-Maleev representation the spin-wave theory of the quartet state is developed. The spectrum of the lower magnon excitations consists of three degenerate modes with the energy gap $Δ=0.17J$. The ground state energy per spin $E/N =-0.6J$. This preprint repeats in the main the previous one but it contains calculations of the basic corrections and therefore has complete character.

cond-mat↗
arXiv1994

Luttinger States at the Edge

An effective wavefunction for the edge excitations in the Fractional quantum Hall effect can be found by dimensionally reducing the bulk wavefunction. Treated this way the Laughlin $ν=1/(2n+1)$ wavefunction yields a Luttinger model ground state. We identify the edge-electron field with a Luttinger hyper-fermion operator, and the edge electron itself with a non-backscattering Bogoliubov quasi-particle. The edge-electron propagator may be calculated directly from the effective wavefunction using the properties of a one-dimensional one-component plasma, provided a prescription is adopted which is sensitive to the extra flux attached to the electrons.

cond-mat↗
arXiv1995

SCHRÖDINGER INVARIANCE IN DISCRETE STOCHASTIC SYSTEMS

Local scale invariance for lattice models is studied using new realizations of the Schrödinger algebra. The two-point function is calculated and it turns out that the result can be reproduced from exact two-point correlation functions evaluated in the stationary state of several simple stochastic models.

cond-mat↗
arXiv1994

Gap Formation Probability of the $α-$ Ensemble

In this paper we employ the continuum approximation of Dyson to determine the asymptotic gap formation probability in the spectrum of $N\times N$ Hermitean random matrices. The associated orthogonal polynomials has weight function, $w(x)=e^{-u(x)},$ where $u(x)=x^α,\;α>0,\;0 1/2$ and depends on $α$ for $0<α<1/2.$

cond-mat↗
arXiv1995

Aspects of ${}^3$He and the Standard Electroweak Model

We describe certain aspects of ${}^3He$ and compare them to related aspects of the standard electroweak model of particle physics. We note various similarities in the order parameter structure, defect structure, interactions with fermions and anomalies in the two systems. Many issues in the condensed matter literature that are often confusing to the particle physics reader and vice versa are clarified.

cond-mat↗
arXiv1995

Spectral Anomaly and High Temperature Superconductors

Spectral anomaly for interacting Fermions is characterized by the spectral function $A([k-k_F],ω)$ satisfying the scaling relation $A(Λ^{y_1} [k-k_F],Λ^{y_2}ω)= Λ^{y_A}A([k-k_F],ω)$, where $y_1$, $y_2$, and $y_A$ are the exponents defining the universality class. For a Fermi liquid $y_1=1$, $y_2=1$, $y_A=-1$; all other values of the exponents are termed anomalous. In this paper, an example for which $y_1=1$, $y_2=1$, but $y_A=α-1$ is considered in detail. Attractive interaction added to such a critical system leads to a novel superconducting state, which is explored and its relevance to high temperature cuprate superconductors is discussed.

cond-mat↗
arXiv1995

Brownian Motion of Solitons in the $Φ^4$ Model

We derive an expression for the correlation function of the random force on a soliton which is consistent with the constraints needed to integrate out the zero modes which appear due to the broken translational symmetry of the soliton solution. It is shown that when the constraint does not commute with the operator which defines the correlation function, i.e. when the operator is not physical, only low frequency phonons contributions may be considered. On the contrary, when the correlation function of the random force on the soliton is constructed with physical operators one may also include in a correct manner the contributions from the optical phonons.

cond-mat↗
arXiv1995

A Variational Ground-State for the $ν=2/3$ Fractional Quantum Hall Regime

A variational $ν=2/3$ state, which unifies the sharp edge picture of MacDonald with the soft edge picture of Chang and of Beenakker is presented and studied in detail. Using an exact relation between correlation functions of this state and those of the Laughlin $ν=1/3$ wavefunction, the correlation functions of the $ν=2/3$ state are determined via a classical Monte Carlo calculation, for systems up to $50$ electrons. It is found that as a function of the slope of the confining potential there is a sharp transition of the ground state from one description to the other. This transition should be observable in tunneling experiments through quantum dots.

cond-mat↗
arXiv1996

Complete Wiener-Hopf Solution of the X-Ray Edge Problem

We present a complete solution of the soft x-ray edge problem within a field-theoretic approach based on the Wiener-Hopf infinite-time technique. We derive for the first time within this approach critical asymptotics of all the relevant quantities for the x-ray problem as well as their nonuniversal prefactors. Thereby we obtain the most complete field-theoretic solution of the problem with a number of new experimentally relevant results. We make thorough comparison of the proposed Wiener-Hopf technique with other approaches based on finite-time methods. It is proven that the Fredholm, finite-time solution converges smoothly to the Wiener-Hopf one and that the latter is stable with respect to perturbations in the long-time limit. Further on we disclose a wide interval of intermediate times showing quasicritical behavior deviating from the Wiener-Hopf one. The quasicritical behavior of the core-hole Green function is derived exactly from the Wiener-Hopf solution and the quasicritical exponent is shown to match the result of Nozières and De Dominicis. The reasons for the quasicritical behavior and the way of a crossover to the infinite-time solution are expounded and the physical relevance of the Nozières and De Dominicis as well as of the Winer-Hopf results are discussed.

cond-mat↗
arXiv1997

Gauge-theory approach to planar doped antiferromagnets and external magnetic fields

A review is given of a relativistic non-Abelian gauge theory approach to the physics of spin-charge separation in doped quantum antiferromagnetic planar systems, proposed recently by the authors. Emphasis is put on the effects of constant external magnetic fields on excitations about the superconducting state in the model. The electrically-charged Dirac fermions (holons), describing excitations about specific points on the fermi surface, e.g. those corresponding to the nodes of a d-wave superconducting gap in high-$T_c$ cuprates, condense, resulting in the opening of a Kosterlitz-Thouless-like gap (KT) at such nodes. In the presence of strong external magnetic fields at the surface regions of the planar superconductor, in the direction perpendicular to the superconducting planes, these KT gaps appear to be enhanced. Our preliminary analysis, based on analytic Scwhinger-Dyson treatments, seems to indicate that for an even number of Dirac fermion species, required in our model as a result of gauging a particle-hole SU(2) symmetry, Parity or Time Reversal violation does not necessarily occurs.Based on these considerations, we argue that recent experimental findings, concerning thermal conductivity plateaux of quasiparticles in planar high-$T_c$ cuprates in strong external magnetic fields, may indicate the presence of such KT gaps, caused by charged Dirac-fermion excitations in these materials, as suggested in the above model.

cond-mat↗
arXiv1993

Underscreened Kondo Necklace

It has been suggested recently by Gan, Coleman, and Andrei that studying the underscreened Kondo problem may help to understand the nature of magnetism in heavy fermion systems. Motivated by Doniach's work on the S=1/2 Kondo necklace, we introduce the underscreened Kondo necklace models with S>1/2. The underscreened Kondo necklace is the simplest lattice model on which the competition between Kondo spin compensation, and magnetic ordering due to an RKKY-type interaction can be examined. We used the mean-field approximation to determine the phase diagram, and found that the low-temperature phase is always an x-y antiferromagnet. This contention is further supported by the derivation of the exact form of the effective hamiltonian in the limit of very large Kondo coupling: it is found to be an antiferromagnetic x-y model for the residual (S-1/2)-spins. In general, the degree of moment compensation depends on both the Kondo coupling, and on S.

cond-mat↗
arXiv1992

Second-Order Dynamics in the Collective Evolution of Coupled Maps and Automata

We review recent numerical studies and the phenomenology of spatially synchronized collective states in many-body dynamical systems. These states exhibit thermodynamic noise superimposed on the collective, quasiperiodic order parameter evolution with typically one basic irrational frequency. We concentrate on the description of the global temporal properties in terms of second-order difference equations.

cond-mat↗