The geometrically-averaged density of states as a measure of localization

Motivated by current interest in disordered systems of interacting electrons, the effectiveness of the geometrically averaged density of states, $\rho_g(\omega)$, as an order parameter for the Anderson transition is examined. In the context of finite-size systems we examine complications which arise from finite energy resolution. Furthermore we demonstrate that even in infinite systems a decline in $\rho_g(\omega)$ with increasing disorder strength is not uniquely associated with localization.Comment: 8 pages, 8 figures; revised text and figure

Towards analytic description of a transition from weak to strong coupling regime in correlated electron systems. I. Systematic diagrammatic theory with two-particle Green functions

We analyze behavior of correlated electrons described by Hubbard-like models at intermediate and strong coupling. We show that with increasing interaction a pole in a generic two-particle Green function is approached. The pole signals metal-insulator transition at half filling and gives rise to a new vanishing ``Kondo'' scale causing breakdown of weak-coupling perturbation theory. To describe the critical behavior at the metal-insulator transition a novel, self-consistent diagrammatic technique with two-particle Green functions is developed. The theory is based on the linked-cluster expansion for the thermodynamic potential with electron-electron interaction as propagator. Parquet diagrams with a generating functional are derived. Numerical instabilities due to the metal-insulator transition are demonstrated on simplifications of the parquet algebra with ring and ladder series only. A stable numerical solution in the critical region is reached by factorization of singular terms via a low-frequency expansion in the vertex function. We stress the necessity for dynamical vertex renormalizations, missing in the simple approximations, in order to describe the critical, strong-coupling behavior correctly. We propose a simplification of the full parquet approximation by keeping only most divergent terms in the asymptotic strong-coupling region. A qualitatively new, feasible approximation suitable for the description of a transition from weak to strong coupling is obtained.Comment: 17 pages, 4 figures, REVTe

Cumulant expansion of the periodic Anderson model in infinite dimension

The diagrammatic cumulant expansion for the periodic Anderson model with infinite Coulomb repulsion ($U=\infty$) is considered here for an hypercubic lattice of infinite dimension ($d=\infty$). The same type of simplifications obtained by Metzner for the cumulant expansion of the Hubbard model in the limit of $d=\infty$, are shown to be also valid for the periodic Anderson model.Comment: 13 pages, 7 figures.ps. To be published in J. Phys. A: Mathematical and General (1997

The free energy in a magnetic field and the universal scaling equation of state for the three-dimensional Ising model

We have substantially extended the high-temperature and low-magnetic-field (and the related low-temperature and high-magnetic-field) bivariate expansions of the free energy for the conventional three-dimensional Ising model and for a variety of other spin systems generally assumed to belong to the same critical universality class. In particular, we have also derived the analogous expansions for the Ising models with spin s=1,3/2,.. and for the lattice euclidean scalar field theory with quartic self-interaction, on the simple cubic and the body-centered cubic lattices. Our bivariate high-temperature expansions, which extend through K^24, enable us to compute, through the same order, all higher derivatives of the free energy with respect to the field, namely all higher susceptibilities. These data make more accurate checks possible, in critical conditions, both of the scaling and the universality properties with respect to the lattice and the interaction structure and also help to improve an approximate parametric representation of the critical equation of state for the three-dimensional Ising model universality class.Comment: 22 pages, 10 figure

Linked Cluster Expansion Around Mean-Field Theories of Interacting Electrons

A general expansion scheme based on the concept of linked cluster expansion from the theory of classical spin systems is constructed for models of interacting electrons. It is shown that with a suitable variational formulation of mean-field theories at weak (Hartree-Fock) and strong (Hubbard-III) coupling the expansion represents a universal and comprehensive tool for systematic improvements of static mean-field theories. As an example of the general formalism we investigate in detail an analytically tractable series of ring diagrams that correctly capture dynamical fluctuations at weak coupling. We introduce renormalizations of the diagrammatic expansion at various levels and show how the resultant theories are related to other approximations of similar origin. We demonstrate that only fully self-consistent approximations produce global and thermodynamically consistent extensions of static mean field theories. A fully self-consistent theory for the ring diagrams is reached by summing the so-called noncrossing diagrams.Comment: 17 pages, REVTEX, 13 uuencoded postscript figures in 2 separate file

Solitary Waves of Planar Ferromagnets and the Breakdown of the Spin-Polarized Quantum Hall Effect

A branch of uniformly-propagating solitary waves of planar ferromagnets is identified. The energy dispersion and structures of the solitary waves are determined for an isotropic ferromagnet as functions of a conserved momentum. With increasing momentum, their structure undergoes a transition from a form ressembling a droplet of spin-waves to a Skyrmion/anti-Skyrmion pair. An instability to the formation of these solitary waves is shown to provide a mechanism for the electric field-induced breakdown of the spin-polarized quantum Hall effect.Comment: 5 pages, 3 eps-figures, revtex with epsf.tex and multicol.st

Dirac quasiparticles in the mixed state

Energies and wave functions are calculated for d-wave quasiparticles in the mixed state using the formalism of Franz and Tesanovic for the low-lying energy levels. The accuracy of the plane-wave expansion is explored by comparing approximate to exact results for a simplified one-dimensional problem, and the convergence of the plane- wave expansion to the two-dimensional case is studied. The results are used to calculate the low-energy tunneling density of states and the low-temperature specific heat, and these theoretical results are compared to semiclassical treatments and to the available data. Implications for the muon spin resonance measurements of vortex core size are also discussed.Comment: 13 pages, 15 figures, RevTeX. References corrected. A factor of 2 in the results has been corrected, and the conclusions have been update

Triviality problem and the high-temperature expansions of the higher susceptibilities for the Ising and the scalar field models on four-, five- and six-dimensional lattices

High-temperature expansions are presently the only viable approach to the numerical calculation of the higher susceptibilities for the spin and the scalar-field models on high-dimensional lattices. The critical amplitudes of these quantities enter into a sequence of universal amplitude-ratios which determine the critical equation of state. We have obtained a substantial extension through order 24, of the high-temperature expansions of the free energy (in presence of a magnetic field) for the Ising models with spin s >= 1/2 and for the lattice scalar field theory with quartic self-interaction, on the simple-cubic and the body-centered-cubic lattices in four, five and six spatial dimensions. A numerical analysis of the higher susceptibilities obtained from these expansions, yields results consistent with the widely accepted ideas, based on the renormalization group and the constructive approach to Euclidean quantum field theory, concerning the no-interaction ("triviality") property of the continuum (scaling) limit of spin-s Ising and lattice scalar-field models at and above the upper critical dimensionality.Comment: 17 pages, 10 figure