536 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
Phase Diagram for Anderson Disorder: beyond Single-Parameter Scaling
The Anderson model for independent electrons in a disordered potential is
transformed analytically and exactly to a basis of random extended states
leading to a variant of augmented space. In addition to the widely-accepted
phase diagrams in all physical dimensions, a plethora of additional, weaker
Anderson transitions are found, characterized by the long-distance behavior of
states. Critical disorders are found for Anderson transitions at which the
asymptotically dominant sector of augmented space changes for all states at the
same disorder. At fixed disorder, critical energies are also found at which the
localization properties of states are singular. Under the approximation of
single-parameter scaling, this phase diagram reduces to the widely-accepted one
in 1, 2 and 3 dimensions. In two dimensions, in addition to the Anderson
transition at infinitesimal disorder, there is a transition between two
localized states, characterized by a change in the nature of wave function
decay.Comment: 51 pages including 4 figures, revised 30 November 200
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
On the Absence of Spurious Eigenstates in an Iterative Algorithm Proposed By Waxman
We discuss a remarkable property of an iterative algorithm for eigenvalue
problems recently advanced by Waxman that constitutes a clear advantage over
other iterative procedures. In quantum mechanics, as well as in other fields,
it is often necessary to deal with operators exhibiting both a continuum and a
discrete spectrum. For this kind of operators, the problem of identifying
spurious eigenpairs which appear in iterative algorithms like the Lanczos
algorithm does not occur in the algorithm proposed by Waxman
Unusual localisation effects in quantum percolation
We present a detailed study of the quantum site percolation problem on simple
cubic lattices, thereby focussing on the statistics of the local density of
states and the spatial structure of the single particle wavefunctions. Using
the Kernel Polynomial Method we refine previous studies of the metal-insulator
transition and demonstrate the non-monotonic energy dependence of the quantum
percolation threshold. Remarkably, the data indicates a ``fragmentation'' of
the spectrum into extended and localised states. In addition, the observation
of a chequerboard-like structure of the wavefunctions at the band centre can be
interpreted as anomalous localisation.Comment: 5 pages, 7 figure
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
Assessment of the GW Approximation using Hubbard Chains
We investigate the performance of the GW approximation by comparison to exact results for small model systems. The role of the chemical potentials in Dyson's equation as well as the consequences of numerical resonance broadening are examined, and we show how a proper treatment can improve computational implementations of many-body perturbation theory in general. GW and exchange-only calculations are performed over a wide range of fractional band fillings and correlation strengths. We thus identify the physical situations where these schemes are applicable
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
Echolocation by Quasiparticles
It is shown that the local density of states (LDOS), measured in an Scanning
Tunneling Microscopy (STM) experiment, at a single tip position contains
oscillations as a function of Energy, due to quasiparticle interference, which
is related to the positions of nearby scatterers. We propose a method of STM
data analysis based on this idea, which can be used to locate the scatterers.
In the case of a superconductor, the method can potentially distinguish the
nature of the scattering by a particular impurity.Comment: 4+ page
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
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