158 research outputs found
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
Damping of zero sound in Luttinger liquids
We calculate the damping gamma_q of collective density oscillations (zero
sound) in a one-dimensional Fermi gas with dimensionless forward scattering
interaction F and quadratic energy dispersion k^2 / 2 m at zero temperature.
For wave-vectors | q| /k_F small compared with F we find to leading order
gamma_q = v_F^{-1} m^{-2} Y (F) | q |^3, where v_F is the Fermi velocity, k_F
is the Fermi wave-vector, and Y (F) is proportional to F^3 for small F. We also
show that zero-sound damping leads to a finite maximum proportional to |k - k_F
|^{-2 + 2 eta} of the charge peak in the single-particle spectral function,
where eta is the anomalous dimension. Our prediction agrees with photoemission
data for the blue bronze K_{0.3}MoO_3.Comment: final version as published; with more technical details; we have
added a discussion of recent work which appeared after our initial cond-mat
posting; 13 pages, 5 figure
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.
Dynamic Many-Body Theory. II. Dynamics of Strongly Correlated Fermi Fluids
We develop a systematic theory of multi-particle excitations in strongly
interacting Fermi systems. Our work is the generalization of the time-honored
work by Jackson, Feenberg, and Campbell for bosons, that provides, in its most
advanced implementation, quantitative predictions for the dynamic structure
function in the whole experimentally accessible energy/momentum regime. Our
view is that the same physical effects -- namely fluctuations of the wave
function at an atomic length scale -- are responsible for the correct
energetics of the excitations in both Bose and Fermi fluids. Besides a
comprehensive derivation of the fermion version of the theory and discussion of
the approximations made, we present results for homogeneous He-3 and electrons
in three dimensions. We find indeed a significant lowering of the zero sound
mode in He-3 and a broadening of the collective mode due to the coupling to
particle-hole excitations in good agreement with experiments. The most visible
effect in electronic systems is the appearance of a ``double-plasmon''
excitation.Comment: submitted to Phys. Rev.
Nonlocal density functionals and the linear response of the homogeneous electron gas
The known and usable truly nonlocal functionals for exchange-correlation
energy of the inhomogeneous electron gas are the ADA (average density
approximation) and the WDA (weighted density approximation). ADA, by design,
yields the correct linear response function of the uniform electron gas. WDA is
constructed so that it is exact in the limit of one-electron systems. We derive
an expression for the linear response of the uniform gas in the WDA, and
calculate it for several flavors of WDA. We then compare the results with the
Monte-Carlo data on the exchange-correlation local field correction, and
identify the weak points of conventional WDA in the homogeneous limit. We
suggest how the WDA can be modified to improve the response function. The
resulting approximation is a good one in both opposite limits, and should be
useful for practical nonlocal density functional calculations.Comment: 4 pages, two eps figures embedde
Exact exchange potential evaluated solely from occupied Kohn-Sham and Hartree-Fock solutions
The reported new algorithm determines the exact exchange potential v_x in a
iterative way using energy and orbital shifts (ES, OS) obtained - with
finite-difference formulas - from the solutions (occupied orbitals and their
energies) of the Hartree-Fock-like equation and the Kohn-Sham-like equation,
the former used for the initial approximation to v_x and the latter - for
increments of ES and OS due to subsequent changes of v_x. Thus, solution of the
differential equations for OS, used by Kummel and Perdew (KP) [Phys. Rev. Lett.
90, 043004 (2003)], is avoided. The iterated exchange potential, expressed in
terms of ES and OS, is improved by modifying ES at odd iteration steps and OS
at even steps. The modification formulas are related to the OEP equation
(satisfied at convergence) written as the condition of vanishing density shift
(DS) - they are obtained, respectively, by enforcing its satisfaction through
corrections to approximate OS and by determining optimal ES that minimize the
DS norm. The proposed method, successfully tested for several closed-(sub)shell
atoms, from Be to Kr, within the DFT exchange-only approximation, proves highly
efficient. The calculations using pseudospectral method for representing
orbitals give iterative sequences of approximate exchange potentials (starting
with the Krieger-Li-Iafrate approximation) that rapidly approach the exact v_x
so that, for Ne, Ar and Zn, the corresponding DS norm becomes less than 10^{-6}
after 13, 13 and 9 iteration steps for a given electron density. In
self-consistent density calculations, orbital energies of 10^{-4} Hartree
accuracy are obtained for these atoms after, respectively, 9, 12 and 12 density
iteration steps, each involving just 2 steps of v_x iteration, while the
accuracy limit of 10^{-6}--10^{-7} Hartree is reached after 20 density
iterations.Comment: 21 pages, 5 figures, 3 table
Analytical expressions for the charge-charge local-field factor and the exchange-correlation kernel of a two-dimensional electron gas
We present an analytical expression for the static many-body local field
factor of a homogeneous two-dimensional electron gas, which
reproduces Diffusion Monte Carlo data and embodies the exact asymptotic
behaviors at both small and large wave number . This allows us to also
provide a closed-form expression for the exchange and correlation kernel
, which represents a key input for density functional studies of
inhomogeneous systems.Comment: 5 pages, 3 figure
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.
Nonuniqueness of the Potentials of Spin-Density-Functional Theory
It is shown that, contrary to widely held beliefs, the potentials of
spin-density-functional theory (SDFT) are not unique functionals of the spin
densities. Explicit examples of distinct sets of potentials with the same
ground-state densities are constructed, and general arguments that uniqueness
should not occur in SDFT and other generalized density-functional theories are
given. As a consequence, various types of applications of SDFT require
significant corrections or modifications.Comment: 4 pages, no figure
Correlation energies of inhomogeneous many-electron systems
We generalize the uniform-gas correlation energy formalism of Singwi, Tosi,
Land and Sjolander to the case of an arbitrary inhomogeneous many-particle
system. For jellium slabs of finite thickness with a self-consistent LDA
groundstate Kohn-Sham potential as input, our numerical results for the
correlation energy agree well with diffusion Monte Carlo results. For a helium
atom we also obtain a good correlation energy.Comment: 4 pages,1 figur
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