190 research outputs found
Simple model of the static exchange-correlation kernel of a uniform electron gas with long-range electron-electron interaction
A simple approximate expression in real and reciprocal spaces is given for
the static exchange-correlation kernel of a uniform electron gas interacting
with the long-range part only of the Coulomb interaction. This expression
interpolates between the exact asymptotic behaviors of this kernel at small and
large wave vectors which in turn requires, among other thing, information from
the momentum distribution of the uniform electron gas with the same interaction
that have been calculated in the G0W0 approximation. This exchange-correlation
kernel as well as its complement analogue associated to the short-range part of
the Coulomb interaction are more local than the Coulombic exchange-correlation
kernel and constitute potential ingredients in approximations for recent
adiabatic connection fluctuation-dissipation and/or density functional theory
approaches of the electronic correlation problem based on a separate treatment
of long-range and short-range interaction effects.Comment: 14 pages, 14 figures, to be published in Phys. Rev.
Metal–insulator transition in 2D as a quantum phase transition
We discuss the metal–insulator transition phenomenon in two dimensions in
terms of a quantum critical point that controls a range of the low temperature
insulator region as well as the usual quantum critical sector. We show that
this extended range of criticality permits a determination of both the dynamical
critical exponent z and the correlation length critical exponent ν from published
data from a single experiment in the insulator critical region. The resulting
value of the product zν is consistent with the temperature dependence of the
resistance in the quantum critical sector. This provides strong quantitative
evidence for the presence of a quantum critical point
Disorder-Induced Resistive Anomaly Near Ferromagnetic Phase Transitions
We show that the resistivity rho(T) of disordered ferromagnets near, and
above, the Curie temperature T_c generically exhibits a stronger anomaly than
the scaling-based Fisher-Langer prediction. Treating transport beyond the
Boltzmann description, we find that within mean-field theory, d\rho/dT exhibits
a |T-T_c|^{-1/2} singularity near T_c. Our results, being solely due to
impurities, are relevant to ferromagnets with low T_c, such as SrRuO3 or
diluted magnetic semiconductors, whose mobility near T_c is limited by
disorder.Comment: 5 pages, 3 figures; V2: with a few clarifications, as publishe
Conserving Approximations in Time-Dependent Density Functional Theory
In the present work we propose a theory for obtaining successively better
approximations to the linear response functions of time-dependent density or
current-density functional theory. The new technique is based on the
variational approach to many-body perturbation theory (MBPT) as developed
during the sixties and later expanded by us in the mid nineties. Due to this
feature the resulting response functions obey a large number of conservation
laws such as particle and momentum conservation and sum rules. The quality of
the obtained results is governed by the physical processes built in through
MBPT but also by the choice of variational expressions. We here present several
conserving response functions of different sophistication to be used in the
calculation of the optical response of solids and nano-scale systems.Comment: 11 pages, 4 figures, revised versio
The on-top pair-correlation density in the homogeneous electron liquid
The ladder theory, in which the Bethe-Goldstone equation for the effective
potential between two scattering particles plays a central role, is well known
for its satisfactory description of the short-range correlations in the
homogeneous electron liquid. By solving exactly the Bethe-Goldstone equation in
the limit of large transfer momentum between two scattering particles, we
obtain accurate results for the on-top pair-correlation density , in both
three dimensions and two dimensions. Furthermore, we prove, in general, the
ladder theory satisfies the cusp condition for the pair-correlation density
at zero distance .Comment: 8 pages, 4 figure
Bosonization of interacting fermions in arbitrary dimension beyond the Gaussian approximation
We use our recently developed functional bosonization approach to bosonize
interacting fermions in arbitrary dimension beyond the Gaussian
approximation. Even in the finite curvature of the energy dispersion at
the Fermi surface gives rise to interactions between the bosons. In higher
dimensions scattering processes describing momentum transfer between different
patches on the Fermi surface (around-the-corner processes) are an additional
source for corrections to the Gaussian approximation. We derive an explicit
expression for the leading correction to the bosonized Hamiltonian and the
irreducible self-energy of the bosonic propagator that takes the finite
curvature as well as around-the-corner processes into account. In the special
case that around-the-corner scattering is negligible, we show that the
self-energy correction to the Gaussian propagator is negligible if the
dimensionless quantities are
small compared with unity for all patches . Here is the cutoff
of the interaction in wave-vector space, is the Fermi wave-vector,
is the chemical potential, is the usual dimensionless Landau
interaction-parameter, and is the {\it{local}} density of
states associated with patch . We also show that the well known
cancellation between vertex- and self-energy corrections in one-dimensional
systems, which is responsible for the fact that the random-phase approximation
for the density-density correlation function is exact in , exists also in
, provided (1) the interaction cutoff is small compared with
, and (2) the energy dispersion is locally linearized at the Fermi the
Fermi surface. Finally, we suggest a new systematic method to calculate
corrections to the RPA, which is based on the perturbative calculation of the
irreducible bosonic self-energy arising from the non-Gaussian terms of the
bosonized Hamiltonian.Comment: The abstract has been rewritten. No major changes in the text
Nucleus-Electron Model for States Changing from a Liquid Metal to a Plasma and the Saha Equation
We extend the quantal hypernetted-chain (QHNC) method, which has been proved
to yield accurate results for liquid metals, to treat a partially ionized
plasma. In a plasma, the electrons change from a quantum to a classical fluid
gradually with increasing temperature; the QHNC method applied to the electron
gas is in fact able to provide the electron-electron correlation at arbitrary
temperature. As an illustrating example of this approach, we investigate how
liquid rubidium becomes a plasma by increasing the temperature from 0 to 30 eV
at a fixed normal ion-density . The electron-ion
radial distribution function (RDF) in liquid Rb has distinct inner-core and
outer-core parts. Even at a temperature of 1 eV, this clear distinction remains
as a characteristic of a liquid metal. At a temperature of 3 eV, this
distinction disappears, and rubidium becomes a plasma with the ionization 1.21.
The temperature variations of bound levels in each ion and the average
ionization are calculated in Rb plasmas at the same time. Using the
density-functional theory, we also derive the Saha equation applicable even to
a high-density plasma at low temperatures. The QHNC method provides a procedure
to solve this Saha equation with ease by using a recursive formula; the charge
population of differently ionized species are obtained in Rb plasmas at several
temperatures. In this way, it is shown that, with the atomic number as the only
input, the QHNC method produces the average ionization, the electron-ion and
ion-ion RDF's, and the charge population which are consistent with the atomic
structure of each ion for a partially ionized plasma.Comment: 28 pages(TeX) and 11 figures (PS
Structure Factor and Electronic Structure of Compressed Liquid Rubidium
We have applied the quantal hypernetted-chain equations in combination with
the Rosenfeld bridge-functional to calculate the atomic and the electronic
structure of compressed liquid-rubidium under high pressure (0.2, 2.5, 3.9, and
6.1 GPa); the calculated structure factors are in good agreement with
experimental results measured by Tsuji et al. along the melting curve. We found
that the Rb-pseudoatom remains under these high pressures almost unchanged with
respect to the pseudoatom at room pressure; thus, the effective ion-ion
interaction is practically the same for all pressure-values. We observe that
all structure factors calculated for this pressure-variation coincide almost
into a single curve if wavenumbers are scaled in units of the Wigner-Seitz
radius although no corresponding scaling feature is observed in the
effective ion-ion interaction.This scaling property of the structure factors
signifies that the compression in liquid-rubidium is uniform with increasing
pressure; in absolute Q-values this means that the first peak-position ()
of the structure factor increases proportionally to ( being the
specific volume per ion), as was experimentally observed by Tsuji et al.Comment: 18 pages, 11 figure
The effective mass and g-factor of the strongly correlated 2-D electron fluid. Evidence for a coupled-valley condensate in the Si system
The effective mass m*, and the Lande g-factor of the uniform 2-D electron
fluid (2DEF) are calculated as a function of the spin polarization zeta, and
the density parameter r_s, using a non-perturbative analytic approach. Our
theory is in good accord with the m*g* data of Zhu et al. for zeta=0 for the
GaAs-2DEF, and striking agreement with the data of Shashkin et al for the
Si-2DEF.
While g* is enhanced in GaAs, m* is enhanced in Si. The latter arises from
singlet-pair excitations in the two valleys forming a coupled-valley state
occurring at the critical density of ~1.10^{11}$ e/cm^2.Comment: New version#4 is the July 2004 published version (Europhysics
Letters
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