142 research outputs found
Structure of the Local-field factor of the 2-D electron fluid. Possible evidence for correlated scattering of electron pairs
The static local-field factor (LFF) of the 2-D electron fluid is calculated
{\it nonperturbatively} using a mapping to a classical Coulomb fluid
Phys. Rev. Lett., {\bf 87}, 206. The LFF for the paramagnetic
fluid {\it differs markedly} from perturbation theory where a maximum near
2 is expected. Our LFF has a quasi-linear small-k region leading to a
maximum close to 3, in agreent with currently available quantum Monte
Carlo data. The structure in the LFF and its dependence on the density and
temperature are interpretted as a signature of correlated scattering of
electron pairs of opposite spin.The lack of structure at implies
weakened Friedel oscillations, Kohn anomalies etc.Comment: 4 pages, 3 figures, version 2 of condmat/0304034, see
http://nrcphy1.phy.nrc.ca/ims/qp/chandre/chnc/ Changs in the text, figure 2
and updated reference
Kirzhnits gradient expansion for a D-dimensional Fermi gas
For an ideal D-dimensional Fermi gas under generic external confinement we
derive the correcting coefficient of the von Weizsacker term in the
kinetic energy density. To obtain this coefficient we use the Kirzhnits
semiclassical expansion of the number operator up to the second order in the
Planck constant . Within this simple and direct approach we determine
the differential equation of the density profile and the density functional of
the Fermi gas. In the case D=2 we find that the Kirzhnits gradient corrections
vanish to all order in .Comment: 6 pages, 0 figures, accepted for publication in J. Phys. A: Math.
Theo
Hartree-Fock method posed as a density-functional theory: Application to the Be atom
The Hartree-Fock ground-state energy and electron density are first shown to be derivable from a local one-body effective potential v(r). As a nontrivial example, attention is then focused on the Be atom and isoelectronic atomic ions, the wave functions being written in terms of the density amplitude and phase. Some related general comments on the two-level one-dimensional system are included; kinetic-energy density is shown to be a local functional of electron density generated by the harmonic-oscillator potential
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.
Scaling in the correlation energies of two-dimensional artificial atoms
We find an unexpected scaling in the correlation energy of artificial atoms,
i.e., harmonically confined two-dimensional quantum dots. The scaling relation
is found through extensive numerical examinations including Hartree-Fock,
variational quantum Monte Carlo, density-functional, and full
configuration-interaction calculations. We show that the correlation energy,
i.e., the true ground-state total energy subtracted by the Hartree-Fock total
energy, follows a simple function of the Coulomb energy, confimenent strength
and, the number of electrons. We find an analytic expression for this function,
as well as for the correlation energy per particle and for the ratio between
the correlation and total energies. Our tests for independent diffusion Monte
Carlo and coupled-cluster results for quantum dots -- including open-shell data
-- confirm the generality of the obtained scaling. As the scaling is also well
applicable to 100 electrons, our results give interesting prospects
for the development of correlation functionals within density-functional
theory.Comment: Accepted to Journal of Physics: Condensed Matte
Exchange-correlation energy densities for two-dimensional systems from quantum dot ground-states
In this paper we present a new approach how to extract polarization-dependent
exchange-correlation energy densities for two-dimensional systems from
reference densities and energies of quantum dots provided by exact
diagonalization. Compared with results from literature we find systematic
corrections for all polarizations in the regime of high densities.Comment: 7 figures. submitted to Phys. Rev.
Density-Functional Theory of Quantum Freezing: Sensitivity to Liquid-State Structure and Statistics
Density-functional theory is applied to compute the ground-state energies of
quantum hard-sphere solids. The modified weighted-density approximation is used
to map both the Bose and the Fermi solid onto a corresponding uniform Bose
liquid, assuming negligible exchange for the Fermi solid. The required
liquid-state input data are obtained from a paired phonon analysis and the
Feynman approximation, connecting the static structure factor and the linear
response function. The Fermi liquid is treated by the Wu-Feenberg cluster
expansion, which approximately accounts for the effects of antisymmetry.
Liquid-solid transitions for both systems are obtained with no adjustment of
input data. Limited quantitative agreement with simulation indicates a need for
further improvement of the liquid-state input through practical alternatives to
the Feynman approximation.Comment: IOP-TeX, 21 pages + 7 figures, to appear, J. Phys.: Condens. Matte
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
Exchange and correlation energies of ground states of atoms and molecules in strong magnetic fields
Using a Hartree-Fock mesh method and a configuration interaction approach
based on a generalized Gaussian basis set we investigate the behaviour of the
exchange and correlation energies of small atoms and molecules, namely th e
helium and lithium atom as well as the hydrogen molecule, in the presence of a
magnetic field covering the regime B=0-100a.u. In general the importance of the
exchange energy to the binding properties of at oms or molecules increases
strongly with increasing field strength. This is due to the spin-flip
transitions and in particular due to the contributions of the tightly bound
hydrogenic state s which are involved in the corresponding ground states of
different symmetries. In contrast to the exchange energy the correlation energy
becomes less relevant with increasing field strength. This holds for the
individual configurations constituting the ground state and for the crossovers
of the global ground state.Comment: 4 Figures acc.f.publ.in Phys.Rev.
Dynamic correlations in symmetric electron-electron and electron-hole bilayers
The ground-state behavior of the symmetric electron-electron and
electron-hole bilayers is studied by including dynamic correlation effects
within the quantum version of Singwi, Tosi, Land, and Sjolander (qSTLS) theory.
The static pair-correlation functions, the local-field correction factors, and
the ground-state energy are calculated over a wide range of carrier density and
layer spacing. The possibility of a phase transition into a density-modulated
ground state is also investigated. Results for both the electron-electron and
electron-hole bilayers are compared with those of recent diffusion Monte Carlo
(DMC) simulation studies. We find that the qSTLS results differ markedly from
those of the conventional STLS approach and compare in the overall more
favorably with the DMC predictions. An important result is that the qSTLS
theory signals a phase transition from the liquid to the coupled Wigner crystal
ground state, in both the electron-electron and electron-hole bilayers, below a
critical density and in the close proximity of layers (d <~ r_sa_0^*), in
qualitative agreement with the findings of the DMC simulations.Comment: 13 pages, 11 figures, 2 table
- âŠ