Density Matrix Perturbation Theory

An expansion method for perturbation of the zero temperature grand canonical density matrix is introduced. The method achieves quadratically convergent recursions that yield the response of the zero temperature density matrix upon variation of the Hamiltonian. The technique allows treatment of embedded quantum subsystems with a computational cost scaling linearly with the size of the perturbed region, O(N_pert.), and as O(1) with the total system size. It also allows direct computation of the density matrix response functions to any order with linear scaling effort. Energy expressions to 4th order based on only first and second order density matrix response are given.Comment: 4 pages, 2 figure

Site dilution of quantum spins in the honeycomb lattice

We discuss the effect of site dilution on both the magnetization and the density of states of quantum spins in the honeycomb lattice, described by the antiferromagnetic Heisenberg spin-S model. For this purpose a real-space Bogoliubov-Valatin transformation is used. In this work we show that for the S>1/2 the system can be analyzed in terms of linear spin wave theory. For spin S=1/2, however, the linear spin wave approximation breaks down. In this case, we have studied the effect of dilution on the staggered magnetization using the Stochastic Series Expansion Monte Carlo method. Two main results are to be stressed from the Monte Carlo method: (i) a better value for the staggered magnetization of the undiluted system, m=0.2677(6); (ii) a finite value of the staggered magnetization of the percolating cluster at the classical percolation threshold, showing that there is no quantum critical transition driven by dilution in the Heisenberg model. In the solution of the problem using linear the spin wave method we pay special attention to the presence of zero energy modes. Using a combination of linear spin wave analysis and the recursion method we were able to obtain the thermodynamic limit behavior of the density of states for both the square and the honeycomb lattices. We have used both the staggered magnetization and the density of states to analyze neutron scattering experiments and Neel temperature measurements on quasi-two- -dimensional honeycomb systems. Our results are in quantitative agreement with experimental results on Mn_pZn_{1-p}PS_3 and on the Ba(Ni_pMg_{1-p})_2V_2O_8.Comment: 21 pages (REVTEX), 16 figure

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

Non-magnetic impurities in two dimensional superconductors

A numerical approach to disordered 2D superconductors described by BCS mean field theory is outlined. The energy gap and the superfluid density at zero temperature and the quasiparticle density of states are studied. The method involves approximate self-consistent solutions of the Bogolubov-de$\,$Gennes equations on finite square lattices. Where comparison is possible, the results of standard analytic approaches to this problem are reproduced. Detailed modeling of impurity effects is practical using this approach. The {\it range} of the impurity potential is shown to be of {\it quantitative importance} in the case of strong potential scatterers. We discuss the implications for experiments, such as the rapid suppression of superconductivity by Zn doping in Copper-Oxide superconductors.Comment: 16 pages, latex, 8 figures( available upon request

How to escape Aharonov-Bohm cages ?

We study the effect of disorder and interactions on a recently proposed magnetic field induced localization mechanism. We show that both partially destroy the extreme confinement of the excitations occuring in the pure case and give rise to unusual behavior. We also point out the role of the edge states that allows for a propagation of the electrons in these systems.Comment: 22 pages, 20 EPS figure

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

Microscopic self-consistent theory of Josephson junctions including dynamical electron correlations

We formulate a fully self-consistent, microscopic model to study the retardation and correlation effects of the barrier within a Josephson junction. The junction is described by a series of planes, with electronic correlation included through a local self energy for each plane. We calculate current-phase relationships for various junctions, which include non-magnetic impurities in the barrier region, or an interfacial scattering potential. Our results indicate that the linear response of the supercurrent to phase across the barrier region is a good, but not exact indicator of the critical current. Our calculations of the local density of states show the current-carrying Andreev bound states and their energy evolution with the phase difference across the junction. We calculate the figure of merit for a Josephson junction, which is the product of the critical current, Ic, and the normal state resistance, R(N), for junctions with different barrier materials. The normal state resistance is calculated using the Kubo formula, for a system with zero current flow and no superconducting order. Semiclassical calculations would predict that these two quantities are determined by the transmission probabilities of electrons in such a way that the product is constant for a given superconductor at fixed temperature. Our self-consistent solutions for different types of barrier indicate that this is not the case. We suggest some forms of barrier which could increase the Ic.R(N) product, and hence improve the frequency response of a Josephson device.Comment: 46 pages, 21 figure

Binding of holes and pair spectral function in the t-J model

Clusters of the two-dimensionnal t--J model with 2 holes and up to 26 sites are diagonalized using a Lanczos algorithm. The behaviour of the binding energy with system size suggests the existence of a finite critical value of J above which binding occurs in the bulk. Only the d-wave pair field operator acting on the Heisenberg GS has a finite overlap with the 2 hole ground state for all the clusters considered. The related spectral function associated with the propagation of a d-wave (spin singlet) pair of holes in the antiferromagnetic background is calculated. The quasiparticle peak at the bottom of the spectrum as well as some structure appearing above the peak survive with increasing cluster size. Although no simple scaling law was found for the quasiparticle weight the data strongly suggest that this weight is finite in the bulk limit and is roughly proportional to the antiferromagnetic coupling J (for J<1).Comment: Report LPQTH-93/01, 18 pages (REVTEX), 8 postscript files include

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.

Structural and chemical embrittlement of grain boundaries by impurities: a general theory and first principles calculations for copper

First principles calculations of the Sigma 5 (310)[001] symmetric tilt grain boundary in Cu with Bi, Na, and Ag substitutional impurities provide evidence that in the phenomenon of Bi embrittlement of Cu grain boundaries electronic effects do not play a major role; on the contrary, the embrittlement is mostly a structural or "size" effect. Na is predicted to be nearly as good an embrittler as Bi, whereas Ag does not embrittle the boundary in agreement with experiment. While we reject the prevailing view that "electronic" effects (i.e., charge transfer) are responsible for embrittlement, we do not exclude the role of chemistry. However numerical results show a striking equivalence between the alkali metal Na and the semi metal Bi, small differences being accounted for by their contrasting "size" and "softness" (defined here). In order to separate structural and chemical effects unambiguously if not uniquely, we model the embrittlement process by taking the system of grain boundary and free surfaces through a sequence of precisely defined gedanken processes; each of these representing a putative mechanism. We thereby identify three mechanisms of embrittlement by substitutional impurities, two of which survive in the case of embrittlement or cohesion enhancement by interstitials. Two of the three are purely structural and the third contains both structural and chemical elements that by their very nature cannot be further unravelled. We are able to take the systems we study through each of these stages by explicit computer simulations and assess the contribution of each to the nett reduction in intergranular cohesion. The conclusion we reach is that embrittlement by both Bi and Na is almost exclusively structural in origin; that is, the embrittlement is a size effect.Comment: 13 pages, 5 figures; Accepted in Phys. Rev.