VOLUME 84, NUMBER 5
P H Y S I C A L R E V I E W L E T T E R S
31 JANUARY 2000
and temperature T and shown that it quantitatively recovers
the quantum Monte Carlo PDFs at T 0. The only pa-
rameter is a temperature mapping of the Exc. We have ex-
amined spin-dependent correlation energies, PDFs at zero
and finite T, as well as a simple approximation to the LFC
of the electron response at arbitrary T. The method has
potential applications to nonlocal Exc in DFT, 2D elec-
trons, Bose systems, and extensions to dynamical models
of quantum fluids.
*Electronic address: chandre@cm1.phy.nrc.ca
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FIG. 3. The local-field correction G͑k͒, Eq. (16), to the static
response at T 0 and rs 5. Results shown are as follows:
HNC; Utsumi and Ichimaru (UI) [23]; Vashista and Singwi (VS)
[6]; QMC [14]; Farid et al. (FHER) [8]; and Geldart and Taylor
(GT) [3]. QMC and FHER explicitly base their LFC on the
Lindhard x0 while some of the others are explicitly or implicitly
based on a xI0 (see text).
i.e., quantities outside UI theory. FHER is a fitted form us-
ing over two dozen parameters. The only parameter of the
present model is Tq. It provides approximate G͑k͒ compa-
rable to STLS and UI, involves only a few algebraic steps,
and holds for finite T as well. Thus consider the simplest
LFC, viz., G͑k͒, for a one-component fluid.
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VCou͑k͒G͑k͒ VCou͑k͒ 1 1͞x͑k͒ 2 1͞x0͑k͒ . (15)
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For a classical fluid, x͑k͒ can be expressed in terms of
bS͑k͒. Hence, for the paramagnetic case,
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(Plenum, New York, 1995), p. 635.
VCou͑k͒G͑k͒ VCou͑k͒ 2 ͑T͞n͒ ͓1͞S͑k͒ 2 1͞S0͑k͔͒ .
(16)
In these expressions the x0͑k͒ and S0͑k͒ are based on
a Slater determinant, while the Lindhard function is ap-
plicable to the Hartree case. We display in Fig. 3 the
T 0 LFC for rs 5, and the LFCs of other methods.
The LFCs based on a xI0 calculated with the interacting
density distribution tend to a constant for large k, viz.,
G͑k, 0͒ ! 2͓1 2 g͑0͔͒͞3, while G͑k͒ ! 1 2 g͑0͒. Al-
though the theory of UI is based on a xI0, in practice the
Lindhard x0 is used. The fitted G͑k, 0͒ of FHER is built
to behave like k2 at large k, being an LFC based on the
Lindhard form [24]. It can be shown analytically that the
HNC-LFC tends to 1 2 g͑0͒ for large k, as required. Thus
it is seen that the approximate forms, QMC-LFC, as well
as the HNC-LFC, are in general agreement.
[23] K. Utsumi and S. Ichimaru, Phys. Rev. B 24, 7385 (1981).
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F. J. Rogers and H. E. DeWitt (Plenum, New York, 1987),
p. 463.
In conclusion, we have presented a simple classical map-
ping of a quantum-Fermi liquid for any spin polarization
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