407 research outputs found
Augmented space recursion for partially disordered systems
Off-stoichiometric alloys exhibit partial disorder, in the sense that only
some of the sublattices of the stoichiometric ordered alloy become disordered.
This paper puts forward a generalization of the augmented space recursion (ASR)
(introduced earlier by one of us (Mookerjee et al 1997(*))) for systems with
many atoms per unit cell. In order to justify the convergence properties of ASR
we have studied the convergence of various moments of local density of states
and other physical quantities like Fermi energy and band energy. We have also
looked at the convergence of the magnetic moment of Ni, which is very sensitive
to numerical approximations towards the k-space value 0.6 with the
number of recursion steps prior to termination.Comment: Latex 2e, 21 Pages, 13 Figures, iopb style file attache
Local Phonon Density of States in an Elastic Substrate
The local, eigenfunction-weighted acoustic phonon density of states (DOS)
tensor is calculated for a model substrate consisting of a semi-infinite
isotropic elastic continuum with a stress-free surface. On the surface, the
local DOS is proportional to the square of the frequency, as for the
three-dimensional Debye model, but with a constant of proportionality that is
considerably enhanced compared to the Debye value, a consequence of the
Rayleigh surface modes. The local DOS tensor at the surface is also
anisotropic, as expected. Inside the substrate the local DOS is both spatially
anisotropic and non-quadratic in frequency. However, at large depths, the local
DOS approaches the isotropic Debye value. The results are applied to a Si
substrate.Comment: 7 pages, 2 figures, RevTe
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
Krylov Subspace Method for Molecular Dynamics Simulation based on Large-Scale Electronic Structure Theory
For large scale electronic structure calculation, the Krylov subspace method
is introduced to calculate the one-body density matrix instead of the
eigenstates of given Hamiltonian. This method provides an efficient way to
extract the essential character of the Hamiltonian within a limited number of
basis set. Its validation is confirmed by the convergence property of the
density matrix within the subspace. The following quantities are calculated;
energy, force, density of states, and energy spectrum. Molecular dynamics
simulation of Si(001) surface reconstruction is examined as an example, and the
results reproduce the mechanism of asymmetric surface dimer.Comment: 7 pages, 3 figures; corrected typos; to be published in Journal of
the Phys. Soc. of Japa
An augmented space recursion study of the electronic structure of rough epitaxial overlayers
In this communication we propose the use of the Augmented Space Recursion as
an ideal methodology for the study of electronic and magnetic structures of
rough surfaces, interfaces and overlayers. The method can take into account
roughness, short-ranged clustering effects, surface dilatation and
interdiffusion. We illustrate our method by an application of Fe overlayer on
Ag (100) surface.Comment: 22 pages, Latex, 6 postscript figure
Does Luttinger liquid behaviour survive in an atomic wire on a surface?
We form a highly simplified model of an atomic wire on a surface by the
coupling of two one-dimensional chains, one with electron-electron interactions
to represent the wire and and one with no electron-electron interactions to
represent the surface. We use exact diagonalization techniques to calculate the
eigenstates and response functions of our model, in order to determine both the
nature of the coupling and to what extent the coupling affects the Luttinger
liquid properties we would expect in a purely one-dimensional system. We find
that while there are indeed Luttinger liquid indicators present, some residual
Fermi liquid characteristics remain.Comment: 14 pages, 7 figures. Submitted to J Phys
Linear Algebraic Calculation of Green's function for Large-Scale Electronic Structure Theory
A linear algebraic method named the shifted
conjugate-orthogonal-conjugate-gradient method is introduced for large-scale
electronic structure calculation. The method gives an iterative solver
algorithm of the Green's function and the density matrix without calculating
eigenstates.The problem is reduced to independent linear equations at many
energy points and the calculation is actually carried out only for a single
energy point. The method is robust against the round-off error and the
calculation can reach the machine accuracy. With the observation of residual
vectors, the accuracy can be controlled, microscopically, independently for
each element of the Green's function, and dynamically, at each step in
dynamical simulations. The method is applied to both semiconductor and metal.Comment: 10 pages, 9 figures. To appear in Phys. Rev. B. A PDF file with
better graphics is available at http://fujimac.t.u-tokyo.ac.jp/lses
Exact particle and kinetic energy densities for one-dimensional confined gases of non-interacting fermions
We propose a new method for the evaluation of the particle density and
kinetic pressure profiles in inhomogeneous one-dimensional systems of
non-interacting fermions, and apply it to harmonically confined systems of up
to N=1000 fermions. The method invokes a Green's function operator in
coordinate space, which is handled by techniques originally developed for the
calculation of the density of single-particle states from Green's functions in
the energy domain. In contrast to the Thomas-Fermi (local density)
approximation, the exact profiles under harmonic confinement show negative
local pressure in the tails and a prominent shell structure which may become
accessible to observation in magnetically trapped gases of fermionic alkali
atoms.Comment: 8 pages, 3 figures, accepted for publication in Phys. Rev. Let
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
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
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