A Convergent Method for Calculating the Properties of Many Interacting Electrons

A method is presented for calculating binding energies and other properties of extended interacting systems using the projected density of transitions (PDoT) which is the probability distribution for transitions of different energies induced by a given localized operator, the operator on which the transitions are projected. It is shown that the transition contributing to the PDoT at each energy is the one which disturbs the system least, and so, by projecting on appropriate operators, the binding energies of equilibrium electronic states and the energies of their elementary excitations can be calculated. The PDoT may be expanded as a continued fraction by the recursion method, and as in other cases the continued fraction converges exponentially with the number of arithmetic operations, independent of the size of the system, in contrast to other numerical methods for which the number of operations increases with system size to maintain a given accuracy. These properties are illustrated with a calculation of the binding energies and zone-boundary spin- wave energies for an infinite spin-1/2 Heisenberg chain, which is compared with analytic results for this system and extrapolations from finite rings of spins.Comment: 30 pages, 4 figures, corrected pd

Investigation of a lattice Boltzmann model with a variable speed of sound

A lattice Boltzmann model is considered in which the speed of sound can be varied independently of the other parameters. The range over which the speed of sound can be varied is investigated and good agreement is found between simulations and theory. The onset of nonlinear effects due to variations in the speed of sound is also investigated and good agreement is again found with theory. It is also shown that the fluid viscosity is not altered by changing the speed of sound

Analytic Trajectories for Mobility Edges in the Anderson Model

A basis of Bloch waves, distorted locally by the random potential, is introduced for electrons in the Anderson model. Matrix elements of the Hamiltonian between these distorted waves are averages over infinite numbers of independent site-energies, and so take definite values rather than distributions of values. The transformed Hamiltonian is ordered, and may be interpreted as an itinerant electron interacting with a spin on each site. In this new basis, the distinction between extended and localized states is clear, and edges of the bands of extended states, the mobility edges, are calculated as a function of disorder. In two dimensions these edges have been found in both analytic and numerical applications of tridiagonalization, but they have not been found in analytic approaches based on perturbation theory, or the single-parameter scaling hypothesis; nor have they been detected in numerical approaches based on scaling or critical distributions of level spacing. In both two and three dimensions the mobility edges in this work are found to separate with increasing disorder for all disorders, in contrast with the results of calculation using numerical scaling for three dimensions. The analytic trajectories are compared with recent results of numerical tridiagonalization on samples of over 10^9 sites. This representation of the Anderson model as an ordered interacting system implies that in addition to transitions at mobility edges, the Anderson model contains weaker transitions characterized by critical disorders where the band of extended states decouples from individual sites; and that singularities in the distribution of site energies, rather than its second moment, determine localization properties of the Anderson model.Comment: 32 pages, 2 figure

The Origin of Tunneling Anisotropic Magnetoresistance in Break Junctions

First-principles calculations of electron tunneling transport in Ni and Co break junctions reveal strong dependence of the conductance on the magnetization direction, an effect known as tunneling anisotropic magnetoresistance (TAMR). The origin of this phenomenon stems from resonant states localized in the electrodes near the junction break. The energy and broadening of these states is strongly affected by the magnetization orientation due to spin-orbit coupling, causing TAMR to be sensitive to bias voltage on a scale of a few mV. Our results bear a resemblance to recent experimental data and suggest that TAMR driven by resonant states is a general phenomenon typical for magnetic broken contacts and other experimental geometries where a magnetic tip is used to probe electron transport.Comment: 4 pages, 3 figure

Efficient Recursion Method for Inverting Overlap Matrix

A new O(N) algorithm based on a recursion method, in which the computational effort is proportional to the number of atoms N, is presented for calculating the inverse of an overlap matrix which is needed in electronic structure calculations with the the non-orthogonal localized basis set. This efficient inverting method can be incorporated in several O(N) methods for diagonalization of a generalized secular equation. By studying convergence properties of the 1-norm of an error matrix for diamond and fcc Al, this method is compared to three other O(N) methods (the divide method, Taylor expansion method, and Hotelling's method) with regard to computational accuracy and efficiency within the density functional theory. The test calculations show that the new method is about one-hundred times faster than the divide method in computational time to achieve the same convergence for both diamond and fcc Al, while the Taylor expansion method and Hotelling's method suffer from numerical instabilities in most cases.Comment: 17 pages and 4 figure

Hole motion in the Ising antiferromagnet: an application of the recursion method

We study hole motion in the Ising antiferromagnet using the recursion method. Using the retraceable path approximation we find the hole's Green's function as well as its wavefunction for arbitrary values of $t/J_z$. The effect of small transverse interaction also is taken into account. Our results provide some additional insight into the self-consistent Born approximation.Comment: 8 pages, RevTex, no figures. Accepted for publication in Phys.Rev.

Study of Phase Stability in NiPt Systems

We have studied the problem of phase stability in NiPt alloy system. We have used the augmented space recursion based on the TB-LMTO as the method for studying the electronic structure of the alloys. In particular, we have used the relativistic generalization of our earlier technique. We note that, in order to predict the proper ground state structures and energetics, in addition to relativistic effects, we have to take into account charge transfer effects with precision.Comment: 22 pages, 7 figures. Accepted for publication in JPC

Block bond-order potential as a convergent moments-based method

The theory of a novel bond-order potential, which is based on the block Lanczos algorithm, is presented within an orthogonal tight-binding representation. The block scheme handles automatically the very different character of sigma and pi bonds by introducing block elements, which produces rapid convergence of the energies and forces within insulators, semiconductors, metals, and molecules. The method gives the first convergent results for vacancies in semiconductors using a moments-based method with a low number of moments. Our use of the Lanczos basis simplifies the calculations of the band energy and forces, which allows the application of the method to the molecular dynamics simulations of large systems. As an illustration of this convergent O(N) method we apply the block bond-order potential to the large scale simulation of the deformation of a carbon nanotube.Comment: revtex, 43 pages, 11 figures, submitted to Phys. Rev.

Double Exchange Model for Magnetic Hexaborides

A microscopic theory for rare-earth ferromagnetic hexaborides, such as Eu(1-x)Ca(x)B6, is proposed on the basis of the double-exchange Hamiltonian. In these systems, the reduced carrier concentrations place the Fermi level near the mobility edge, introduced in the spectral density by the disordered spin background. We show that the transport properties such as Hall effect, magnetoresitance, frequency dependent conductivity, and DC resistivity can be quantitatively described within the model. We also make specific predictions for the behavior of the Curie temperature, Tc, as a function of the plasma frequency, omega_p.Comment: 4 pages, 3 figure