79,603 research outputs found
Rayleigh-Schroedinger-Goldstone variational perturbation theory for many fermion systems
We present a Rayleigh-Schroedinger-Goldstone perturbation formalism for many
fermion systems. Based on this formalism, variational perturbation scheme which
goes beyond the Gaussian approximation is developed. In order to go beyond the
Gaussian approximation, we identify a parent Hamiltonian which has an effective
Gaussian vacuum as a variational solution and carry out further perturbation
with respect to the renormalized interaction using Goldstone's expansion.
Perturbation rules for the ground state wavefunctional and energy are found.
Useful commuting relations between operators and the Gaussian wavefunctional
are also found, which could reduce the calculational efforts substantially. As
examples, we calculate the first order correction to the Gaussian
wavefunctional and the second order correction to the ground state of an
electron gas system with the Yukawa-type interaction.Comment: 11pages, 1figur
Uniform Electron Gases. II. The Generalized Local Density Approximation in One Dimension
We introduce a generalization (gLDA) of the traditional Local Density
Approximation (LDA) within density functional theory. The gLDA uses both the
one-electron Seitz radius \rs and a two-electron hole curvature parameter
at each point in space. The gLDA reduces to the LDA when applied to the
infinite homogeneous electron gas but, unlike the LDA, is is also exact for
finite uniform electron gases on spheres. We present an explicit gLDA
functional for the correlation energy of electrons that are confined to a
one-dimensional space and compare its accuracy with LDA, second- and
third-order M{\o}ller-Plesset perturbation energies and exact calculations for
a variety of inhomogeneous systems.Comment: 26 pages, 2 figures, accepted for publication in Journal of Chemical
Physic
Second-order electronic correlation effects in a one-dimensional metal
The Pariser-Parr-Pople (PPP) model of a single-band one-dimensional (1D)
metal is studied at the Hartree-Fock level, and by using the second-order
perturbation theory of the electronic correlation. The PPP model provides an
extension of the Hubbard model by properly accounting for the long-range
character of the electron-electron repulsion. Both finite and infinite version
of the 1D-metal model are considered within the PPP and Hubbard approximations.
Calculated are the second-order electronic-correlation corrections to the total
energy, and to the electronic-energy bands. Our results for the PPP model of 1D
metal show qualitative similarity to the coupled-cluster results for the 3D
electron-gas model. The picture of the 1D-metal model that emerges from the
present study provides a support for the hypothesis that the normal metallic
state of the 1D metal is different from the ground state.Comment: 21 pages, 16 figures; v2: small correction in title, added 3
references, extended and reformulated a few paragraphs (detailed information
at the end of .tex file); added color to figure
Screened exchange corrections to the random phase approximation from many-body perturbation theory
The random phase approximation (RPA) systematically overestimates the
magnitude of the correlation energy and generally underestimates cohesive
energies. This originates in part from the complete lack of exchange terms,
which would otherwise cancel Pauli exclusion principle violating (EPV)
contributions. The uncanceled EPV contributions also manifest themselves in
form of an unphysical negative pair density of spin-parallel electrons close to
electron-electron coalescence.
We follow considerations of many-body perturbation theory to propose an
exchange correction that corrects the largest set of EPV contributions while
having the lowest possible computational complexity. The proposed method
exchanges adjacent particle/hole pairs in the RPA diagrams, considerably
improving the pair density of spin-parallel electrons close to coalescence in
the uniform electron gas (UEG). The accuracy of the correlation energy is
comparable to other variants of Second Order Screened Exchange (SOSEX)
corrections although it is slightly more accurate for the spin-polarized UEG.
Its computational complexity scales as or
in orbital space or real space, respectively. Its memory requirement scales as
Renormalized Second-order Perturbation Theory for The Electron Correlation Energy: Concept, Implementation, and Benchmarks
We present a renormalized second-order perturbation theory (rPT2), based on a
Kohn-Sham (KS) reference state, for the electron correlation energy that
includes the random-phase approximation (RPA), second-order screened exchange
(SOSEX), and renormalized single excitations (rSE). These three terms all
involve a summation of certain types of diagrams to infinite order, and can be
viewed as "renormalization" of the 2nd-order direct, exchange, and single
excitation (SE) terms of Rayleigh-Schr\"odinger perturbation theory based on an
KS reference. In this work we establish the concept of rPT2 and present the
numerical details of our SOSEX and rSE implementations. A preliminary version
of rPT2, in which the renormalized SE (rSE) contribution was treated
approximately, has already been benchmarked for molecular atomization energies
and chemical reaction barrier heights and shows a well balanced performance
[Paier et al, New J. Phys. 14, 043002 (2012)]. In this work, we present a
refined version of rPT2, in which we evaluate the rSE series of diagrams
rigorously. We then extend the benchmark studies to non-covalent interactions,
including the rare-gas dimers, and the S22 and S66 test sets. Despite some
remaining shortcomings, we conclude that rPT2 gives an overall satisfactory
performance across different chemical environments, and is a promising step
towards a generally applicable electronic structure approach.Comment: 16 pages, 11 figure
Antiphased Cyclotron-Magnetoplasma Mode in a Quantum Hall System
An antiphased magnetoplasma (MP) mode in a two-dimensional electron gas
(2DEG) has been studied by means of inelastic light scattering (ILS)
spectroscopy. Unlike the cophased MP mode it is purely quantum excitation which
has no classic plasma analogue. It is found that zero momentum degeneracy for
the antiphased and cophased modes predicted by the first-order perturbation
approach in terms of the {\it e-e} interaction is lifted. The zero momentum
energy gap is determined by a negative correlation shift of the antiphased
mode. This shift, observed experimentally and calculated theoretically within
the second-order perturbation approach, is proportional to the effective
Rydberg constant in a semiconductor material.Comment: Submitted to Phys. Rev.
Explicitly correlated plane waves: Accelerating convergence in periodic wavefunction expansions
We present an investigation into the use of an explicitly correlated plane
wave basis for periodic wavefunction expansions at the level of second-order
M{\o}ller-Plesset perturbation theory (MP2). The convergence of the electronic
correlation energy with respect to the one-electron basis set is investigated
and compared to conventional MP2 theory in a finite homogeneous electron gas
model. In addition to the widely used Slater-type geminal correlation factor,
we also derive and investigate a novel correlation factor that we term
Yukawa-Coulomb. The Yukawa-Coulomb correlation factor is motivated by analytic
results for two electrons in a box and allows for a further improved
convergence of the correlation energies with respect to the employed basis set.
We find the combination of the infinitely delocalized plane waves and local
short-ranged geminals provides a complementary, and rapidly convergent basis
for the description of periodic wavefunctions. We hope that this approach will
expand the scope of discrete wavefunction expansions in periodic systems.Comment: 15 pages, 13 figure
Screened Exchange Corrections to the Random Phase Approximation from Many-Body Perturbation Theory
The random phase approximation (RPA) systematically overestimates the magnitude of the correlation energy and generally underestimates cohesive energies. This originates in part from the complete lack of exchange terms that would otherwise cancel Pauli exclusion principle violating (EPV) contributions. The uncanceled EPV contributions also manifest themselves in form of an unphysical negative pair density of spin parallel electrons close to electron-electron coalescence. We follow considerations of many-body perturbation theory to propose an exchange correction that corrects the largest set of EPV contributions, while having the lowest possible computational complexity. The proposed method exchanges adjacent particle/hole pairs in the RPA diagrams, considerably improving the pair density of spin-parallel electrons close to coalescence in the uniform electron gas (UEG). The accuracy of the correlation energy is comparable to other variants of second-order screened exchange (SOSEX) corrections although it is slightly more accurate for the spin-polarized UEG. Its computational complexity scales as O(N-5) or O(N-4) in orbital space or real space, respectively. Its memory requirement scales as O(N-2)
Variational perturbation approach to the Coulomb electron gas
The efficiency of the variational perturbation theory [Phys. Rev. C {\bf 62},
045503 (2000)] formulated recently for many-particle systems is examined by
calculating the ground state correlation energy of the 3D electron gas with the
Coulomb interaction. The perturbation beyond a variational result can be
carried out systematically by the modified Wick's theorem which defines a
contraction rule about the renormalized perturbation. Utilizing the theorem,
variational ring diagrams of the electron gas are summed up. As a result, the
correlation energy is found to be much closer to the result of the Green's
function Monte Carlo calculation than that of the conventional ring
approximation is.Comment: 4 pages, 3 figure
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