1,431 research outputs found
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,
, 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 with increasing disorder
strength is not uniquely associated with localization.Comment: 8 pages, 8 figures; revised text and figure
Orbital magnetization and Chern number in a supercell framework: Single k-point formula
The key formula for computing the orbital magnetization of a crystalline
system has been recently found [D. Ceresoli, T. Thonhauser, D. Vanderbilt, R.
Resta, Phys. Rev. B {\bf 74}, 024408 (2006)]: it is given in terms of a
Brillouin-zone integral, which is discretized on a reciprocal-space mesh for
numerical implementation. We find here the single -point limit, useful
for large enough supercells, and particularly in the framework of
Car-Parrinello simulations for noncrystalline systems. We validate our formula
on the test case of a crystalline system, where the supercell is chosen as a
large multiple of the elementary cell. We also show that--somewhat
counterintuitively--even the Chern number (in 2d) can be evaluated using a
single Hamiltonian diagonalization.Comment: 4 pages, 3 figures; appendix adde
Spherical Hartree-Fock calculations with linear momentum projection before the variation.Part II: Spectral functions and spectroscopic factors
The hole--spectral functions and from these the spectroscopic factors have
been calculated in an Galilei--invariant way for the ground state wave
functions resulting from spherical Hartree--Fock calculations with projection
onto zero total linear momentum before the variation for the nuclei 4He, 12C,
16O, 28Si, 32S and 40Ca. The results are compared to those of the conventional
approach which uses the ground states resulting from usual spherical
Hartree--Fock calculations subtracting the kinetic energy of the center of mass
motion before the variation and to the results obtained analytically with
oscillator occupations.Comment: 16 pages, 22 postscript figure
A single defect approximation for localized states on random lattices
Geometrical disorder is present in many physical situations giving rise to
eigenvalue problems. The simplest case of diffusion on a random lattice with
fluctuating site connectivities is studied analytically and by exact numerical
diagonalizations. Localization of eigenmodes is shown to be induced by
geometrical defects, that is sites with abnormally low or large connectivities.
We expose a ``single defect approximation'' (SDA) scheme founded on this
mechanism that provides an accurate quantitative description of both extended
and localized regions of the spectrum. We then present a systematic
diagrammatic expansion allowing to use SDA for finite-dimensional problems,
e.g. to determine the localized harmonic modes of amorphous media.Comment: final version as published, 6 pages, 1 ps-figur
Saddle index properties, singular topology, and its relation to thermodynamical singularities for a phi^4 mean field model
We investigate the potential energy surface of a phi^4 model with infinite
range interactions. All stationary points can be uniquely characterized by
three real numbers $\alpha_+, alpha_0, alpha_- with alpha_+ + alpha_0 + alpha_-
= 1, provided that the interaction strength mu is smaller than a critical
value. The saddle index n_s is equal to alpha_0 and its distribution function
has a maximum at n_s^max = 1/3. The density p(e) of stationary points with
energy per particle e, as well as the Euler characteristic chi(e), are singular
at a critical energy e_c(mu), if the external field H is zero. However, e_c(mu)
\neq upsilon_c(mu), where upsilon_c(mu) is the mean potential energy per
particle at the thermodynamic phase transition point T_c. This proves that
previous claims that the topological and thermodynamic transition points
coincide is not valid, in general. Both types of singularities disappear for H
\neq 0. The average saddle index bar{n}_s as function of e decreases
monotonically with e and vanishes at the ground state energy, only. In
contrast, the saddle index n_s as function of the average energy bar{e}(n_s) is
given by n_s(bar{e}) = 1+4bar{e} (for H=0) that vanishes at bar{e} = -1/4 >
upsilon_0, the ground state energy.Comment: 9 PR pages, 6 figure
A Renormalization-Group approach to the Coulomb Gap
The free energy of the Coulomb Gap problem is expanded as a set of Feynman
diagrams, using the standard diagrammatic methods of perturbation theory. The
gap in the one-particle density of states due to long-ranged interactions
corresponds to a renormalization of the two-point vertex function. By
collecting the leading order logarithmic corrections we have derived the
standard result for the density of states in the critical dimension, d=1. This
method, which is shown to be identical to the approach of Thouless, Anderson
and Palmer to spin glasses, allows us to derive the strong-disorder behaviour
of the density of states. The use of the renormalization group allows this
derivation to be extended to all disorders, and the use of an epsilon-expansion
allows the method to be extended to d=2 and d=3. We speculate that the
renormalization group equations can also be derived diagrammatically, allowing
a simple derivation of the crossover behaviour observed in the case of weak
disorder.Comment: 16 pages, LaTeX. Diagrams available on request from
[email protected]. Changes to figure 4 and second half of section
Improved transfer matrix method without numerical instability
A new improved transfer matrix method (TMM) is presented. It is shown that
the method not only overcomes the numerical instability found in the original
TMM, but also greatly improves the scalability of computation. The new improved
TMM has no extra cost of computing time as the length of homogeneous scattering
region becomes large. The comparison between the scattering matrix method(SMM)
and our new TMM is given. It clearly shows that our new method is much faster
than SMM.Comment: 5 pages,3 figure
Orbital magnetization in crystalline solids: Multi-band insulators, Chern insulators, and metals
We derive a multi-band formulation of the orbital magnetization in a normal
periodic insulator (i.e., one in which the Chern invariant, or in 2d the Chern
number, vanishes). Following the approach used recently to develop the
single-band formalism [T. Thonhauser, D. Ceresoli, D. Vanderbilt, and R. Resta,
Phys. Rev. Lett. {\bf 95}, 137205 (2005)], we work in the Wannier
representation and find that the magnetization is comprised of two
contributions, an obvious one associated with the internal circulation of
bulk-like Wannier functions in the interior and an unexpected one arising from
net currents carried by Wannier functions near the surface. Unlike the
single-band case, where each of these contributions is separately
gauge-invariant, in the multi-band formulation only the \emph{sum} of both
terms is gauge-invariant. Our final expression for the orbital magnetization
can be rewritten as a bulk property in terms of Bloch functions, making it
simple to implement in modern code packages. The reciprocal-space expression is
evaluated for 2d model systems and the results are verified by comparing to the
magnetization computed for finite samples cut from the bulk. Finally, while our
formal proof is limited to normal insulators, we also present a heuristic
extension to Chern insulators (having nonzero Chern invariant) and to metals.
The validity of this extension is again tested by comparing to the
magnetization of finite samples cut from the bulk for 2d model systems. We find
excellent agreement, thus providing strong empirical evidence in favor of the
validity of the heuristic formula.Comment: 14 pages, 8 figures. Fixed a typo in appendix
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