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At least 1,207 records · Page 67Linked to original sources
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.

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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.

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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↗
arXiv1996

Coulomb drag in double quantum wells with a perpendicular magnetic field

Momentum transfer due to electron-electron interaction (Coulomb drag) between two quantum wells, separated by a distance $d$, in the presence of a perpendicular magnetic field, is studied at low temperatures. We find besides the well known Shubnikov-de Haas oscillations, which also appear in the drag effect, the momentum transfer is markedly enhanced by the magnetic field.

cond-mat↗
arXiv1997

Estimation of the Doping Dependence of Antiferromagnetism in the Copper Oxide Material

Within the $t$-$J$ model, we study the doping dependence of antiferromagnetism in the copper oxide materials by considering quantum fluctuations of spinons in the random-phase-approximation. The staggered magnetization vanishes around doping $δ=5%$ for a reasonable parameter value $t/J=5$, which is in agreement with the experiments on copper oxide materials.

cond-mat↗
arXiv1996

Partially Solvable Anisotropic t-J Model with Long-Range Interactions

A new anisotropic t-J model in one dimension is proposed which has long-range hopping and exchange. This t-J model is only partially solvable in contrast to known integrable models with long-range interaction. In the high-density limit the model reduces to the XXZ chain with the long-range exchange. Some exact eigenfunctions are shown to be of Jastrow-type if certain conditions for an anisotropy parameter are satisfied. The ground state as well as the excitation spectrum for various cases of the anisotropy parameter and filling are derived numerically. It is found that the Jastrow-type wave function is an excellent trial function for any value of the anisotropy parameter.

cond-mat↗
arXiv1995

Detection of pairing from the extended Aharonov-Bohm period in strongly correlated electron systems

Inspired from Sutherland's work [Phys. Rev. Lett. {\bf 74}, 816 (1995)] on detecting bound spin waves, we propose that bound electron states can be detected from the dependence of interacting electron systems to the Aharonov-Bohm flux in the `extended zone' scheme, where the electron pairing halves the original period $N_a$ flux quanta in a system of linear size $N_a$. Along with the Bethe-ansatz analysis, a numerical implementation for keeping track of the adiabatic flow of energy levels is applied to the attractive/repulsive Hubbard models and the $t-J$ ladder.

cond-mat↗
arXiv1995

Spin Gap of Two-Dimensional Antiferromagnet Representing CaV$_4$O$_9$

We examined a two-dimensional Heisenberg model with two kinds of exchange energies, $J_e$ and $J_c$. This model describes localized spins at vanadium ions in a layer of CaV$_4$O$_9$, for which a spin gap is found by a recent experiment. Comparing the high temperature expansion of the magnetic susceptibility to experimental data, we determined the exchange energies as $J_e \simeq$ 610 K and $J_c \simeq$ 150 K. By the numerical diagonalization we estimated the spin gap as $Δ\sim 0.2J_e \simeq$ 120 K, which consists with the experimental value 107 K. Frustration by finite $J_c$ enhances the spin gap.

cond-mat↗
arXiv1995

Hidden Orders and RVB Formation of the Four-Leg Heisenberg Ladder Model

The ground state of the four-chain Heisenberg ladder model is numerically investigated. Hidden-order correlations suitable for the system are introduced and calculated with an emphasis on the spatially isotropic point, where a corresponding material exists. The existence of a long-range hidden correlation indicates formation of a short-range RVB state in the case of the antiferromagnetic inter-chain coupling. A transition between the phase of the ferromagnetic inter-chain coupling and that of the antiferromagnetic one is discussed.

cond-mat↗
arXiv1995

Haldane Gap and Hidden Order in the S=2 Antiferromagnetic Quantum Spin Chain

We have investigated Haldane's conjecture for the S=2 isotropic antiferromagnetic quantum spin chain with nearest-neighbor exchange J. Using a density matrix renormalization group algorithm for chains up to L=350 spins, we find in the thermodynamic limit a finite spin gap of Delta = 0.085(5)J and a finite spin-spin correlation length xi = 49(1) lattice spacings. We establish the ground state energy per bond to be E_0=-4.761248(1)J. We show that the ground state has a hidden topological order that is revealed in a nonlocal string correlation function. This means that the physics of the S=2 chain can be captured by a valence-bond solid description. We also observe effective free spin-1 states at the ends of an open S=2 chain.

cond-mat↗
arXiv1995

Two-Dimensional Electrons in a Strong Magnetic Field with Disorder: Divergence of the Localization Length

Electrons on a square lattice with half a flux quantum per plaquette are considered. An effective description for the current loops is given by a two-dimensional Dirac theory with random mass. It is shown that the conductivity and the localization length can be calculated from a product of Dirac Green's functions with the {\it same} frequency. This implies that the delocalization of electrons in a magnetic field is due to a critical point in a phase with a spontaneously broken discrete symmetry. The estimation of the localization length is performed for a generalized model with $N$ fermion levels using a $1/N$--expansion and the Schwarz inequality. An argument for the existence of two Hall transition points is given in terms of percolation theory.

cond-mat↗
arXiv1995

Pair correlation functions in one-dimensional correlated-hopping models

We investigate ground-state properties of two correlated-hopping electron models, the Hirsch and the Bariev model. Both models are of recent interest in the context of hole superconductivity. Applying the Lanczos technique to small clusters, we numerically determine the binding energy, the spin gaps, correlation functions, and other properties for various values of the bond-charge interaction parameter. Our results for small systems indicate that pairing is favoured in a certain parameter range. However, in contrast to the Bariev model, superconducting correlations are suppressed in the Hirsch model, for a bond-charge repulsion larger than a critical value.

cond-mat↗
arXiv1995

Analytical Results for Random Band Matrices with Preferential Basis

Using the supersymmetry method we analytically calculate the local density of states, the localiztion length, the generalized inverse participation ratios, and the distribution function of eigenvector components for the superposition of a random band matrix with a strongly fluctuating diagonal matrix. In this way we extend previously known results for ordinary band matrices to the class of random band matrices with preferential basis. Our analytical results are in good agreement with (but more general than) recent numerical findings by Jacquod and Shepelyansky.

cond-mat↗
arXiv1996

Stability of the Bragg glass phase in a layered geometry

We study the stability of the dislocation-free Bragg glass phase in a layered geometry consisting of coupled parallel planes of d=1+1 vortex lines lying within each plane, in the presence of impurity disorder. Using renormalization group, replica variational calculations and physical arguments we show that at temperatures $T<T_G$ the 3D Bragg glass phase is always stable for weak disorder. It undergoes a weakly first order transition into a decoupled 2D vortex glass upon increase of disorder.

cond-mat↗
arXiv1996

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.

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