Wave-number dependence of the static screening function of an interacting electron gas. I. Lowest-order Hartree–Fock corrections

1970 ◽  
Vol 48 (2) ◽  
pp. 155-165 ◽  
Author(s):  
D. J. W. Geldart ◽  
Roger Taylor
Keyword(s):  
Coulomb Interaction ◽  
Ground State ◽  
Electron Gas ◽  
Perturbation Expansion ◽  
Wave Number ◽  
Many Body ◽  
Hartree Fock ◽  
The Many ◽  
Static Screening ◽  
Zero Frequency

The lowest-order Hartree–Fock contributions to the zero frequency screening function are examined for an interacting electron gas in its ground state. Computational methods are developed to treat singularities associated with the bare coulomb interaction and vanishing energy denominators of the many-body perturbation expansion. Numerical results are given. The wave-number dependence in the intermediate (k ~ kF) range differs considerably from that of previous estimates.

Wave-number dependence of the static screening function of an interacting electron gas. II. Higher-order exchange and correlation effects

1970 ◽  
Vol 48 (2) ◽  
pp. 167-181 ◽  
Author(s):  
D. J. W. Geldart ◽  
Roger Taylor
Keyword(s):  
Density Dependence ◽  
Ground State ◽  
Electron Gas ◽  
Perturbation Expansion ◽  
Interpolation Formula ◽  
Higher Order ◽  
Wave Number ◽  
Correlation Effects ◽  
Many Body ◽  
Static Screening

An interpolation formula is suggested for the wave-number and density dependence of the static screening function for an interacting electron gas in its ground state. The approximate screening function simulates a number of properties of the exact screening function which have been established by analysis of its many-body perturbation expansion. The accuracy of the interpolation formula is discussed and is considered to be adequate for practical calculations in the range of intermediate metallic densities.

scholarly journals THE METHOD OF INCREMENTS — A WAVEFUNCTION-BASED AB-INITIO CORRELATION METHOD FOR SOLIDS

2007 ◽  
Vol 21 (13n14) ◽  
pp. 2204-2214 ◽  
Author(s):  
BEATE PAULUS
Keyword(s):  
Experimental Data ◽  
Ab Initio ◽  
Ground State ◽  
Infinite System ◽  
Correlation Energy ◽  
Correlation Method ◽  
Many Body ◽  
Hartree Fock ◽  
The Many ◽  
Good Agreement

The method of increments is a wavefunction-based ab initio correlation method for solids, which explicitly calculates the many-body wavefunction of the system. After a Hartree-Fock treatment of the infinite system the correlation energy of the solid is expanded in terms of localised orbitals or of a group of localised orbitals. The method of increments has been applied to a great variety of materials with a band gap, but in this paper the extension to metals is described. The application to solid mercury is presented, where we achieve very good agreement of the calculated ground-state properties with the experimental data.

EFFECTS OF CORE POLARIZATION AND PAIRING CORRELATIONS ON SOME GROUND-STATE PROPERTIES OF DEFORMED ODD-MASS NUCLEI WITHIN THE HIGHER TAMM–DANCOFF APPROACH

2011 ◽  
Vol 20 (02) ◽  
pp. 252-258 ◽  
Author(s):  
LUDOVIC BONNEAU ◽  
JULIEN LE BLOAS ◽  
PHILIPPE QUENTIN ◽  
NIKOLAY MINKOV
Keyword(s):  
Ground State ◽  
Mean Field ◽  
Energy Difference ◽  
Pair Type ◽  
Many Body ◽  
Hartree Fock ◽  
Ground State Properties ◽  
Pairing Correlations ◽  
The Many ◽  
The Impact

In self-consistent mean-field approaches, the description of odd-mass nuclei requires to break the time-reversal invariance of the underlying one-body hamiltonian. This induces a polarization of the even-even core to which the odd nucleon is added. To properly describe the pairing correlations (in T = 1 and T = 0 channels) in such nuclei, we implement the particle-number conserving Higher Tamm–Dancoff approximation with a residual δ interaction in each isospin channel by restricting the many-body basis to two-particle–two–hole excitations of pair type (nn, pp and np) on top of the Hartree–Fock solution. We apply this approach to the calculation of two ground-state properties of well-deformed nuclei |Tz| = 1 nuclei around 24 Mg and 48 Cr , namely the isovector odd-even binding-energy difference and the magnetic dipole moment, focusing on the impact of pairing correlations.

Improving the convergence of the many‐body perturbation expansion through a convenient summation of exclusion principle violating diagrams

1987 ◽  
Vol 87 (10) ◽  
pp. 5937-5948 ◽  
Author(s):  
Marie‐Bernadette Lepetit ◽  
Jean‐Paul Malrieu
Keyword(s):  
Perturbation Expansion ◽  
Exclusion Principle ◽  
Many Body ◽  
The Many

scholarly journals Non-Hermitian fractional quantum Hall states

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Tsuneya Yoshida ◽  
Koji Kudo ◽  
Yasuhiro Hatsugai
Keyword(s):  
Ground State ◽  
Cold Atoms ◽  
Quantum Hall ◽  
Quantum Zeno Effect ◽  
Many Body ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Zeno Effect ◽  
Quantum Hall States ◽  
The Many

AbstractWe demonstrate the emergence of a topological ordered phase for non-Hermitian systems. Specifically, we elucidate that systems with non-Hermitian two-body interactions show a fractional quantum Hall (FQH) state. The non-Hermitian Hamiltonian is considered to be relevant to cold atoms with dissipation. We conclude the emergence of the non-Hermitian FQH state by the presence of the topological degeneracy and by the many-body Chern number for the ground state multiplet showing Ctot = 1. The robust topological degeneracy against non-Hermiticity arises from the manybody translational symmetry. Furthermore, we discover that the FQH state emerges without any repulsive interactions, which is attributed to a phenomenon reminiscent of the continuous quantum Zeno effect.

Some Properties of Coupled RPA Equations with Separable Interactions

1997 ◽  
Vol 06 (02) ◽  
pp. 251-258 ◽  
Author(s):  
Hideo Sakamoto
Keyword(s):  
Ground State ◽  
Random Phase Approximation ◽  
Strength Function ◽  
Random Phase ◽  
Transition Strength ◽  
Body System ◽  
Many Body ◽  
Hartree Fock ◽  
Secular Equations ◽  
The Stability

We investigate some properties of coupled eigenvalue equations in the random phase approximation for fundamental modes of motion in a nuclear many-body system undergoing several separable two-body interactions. Based on the Sturm's method, a new algorithm is proposed for solving such coupled secular equations and for testing the stability condition of the Hartree-Fock ground state. A transition strength in general is expressed in a compact form and, in a restricted case, a continuous strength function is constructed by averaging with a Lorentzian distribution function.

scholarly journals A hybrid model of Skyrme- and Brueckner-type interactions for neutron star matter

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Soonchul Choi ◽  
Myung-Ki Cheoun ◽  
K S Kim ◽  
Hungchong Kim ◽  
H Sagawa
Keyword(s):  
Neutron Star ◽  
Hybrid Model ◽  
Clear Understanding ◽  
Neutron Skin ◽  
Neutron Star Matter ◽  
Many Body ◽  
Hartree Fock ◽  
Nuclear Incompressibility ◽  
The Many ◽  
Many Body Interactions

Abstract We suggest a hybrid model for neutron star matter to discuss the hyperon puzzle inherent in the 2.0 M$_{\odot}$ of the neutron star. For the nucleon–nucleon ($NN$) interaction, we employ the Skyrme–Hartree–Fock approach based on various Skyrme interaction parameter sets, and take the Brueckner–Hartree–Fock approach for the interactions related to hyperons. For the many-body interactions including hyperons, we make use of the multi-pomeron-exchange model, whose parameters have been adjusted to the data deduced from various hypernuclei properties. For clear understanding of the physics in the hybrid model, we discuss fractional functions of related particles, symmetry energies, and chemical potentials in dense matter. Finally, we investigate the equations of state and mass–radius relation of neutron stars, and show that the hybrid model can properly describe the 2.0 M$_{\odot}$ neutron star mass data with the many-body interaction employed in the hybrid model. Recent tidal deformability data from the gravitational wave observation are also compared to our calculations, especially in terms of the neutron skin of $^{208}$Pb and nuclear incompressibility.

THE SCREENING FUNCTION OF AN INTERACTING ELECTRON GAS

1966 ◽  
Vol 44 (9) ◽  
pp. 2137-2171 ◽  
Author(s):  
D. J. W. Geldart ◽  
S. H. Vosko
Keyword(s):  
Electron Gas ◽  
Substantial Contribution ◽  
Fundamental Relation ◽  
Many Body ◽  
Screening Constant ◽  
Self Energy ◽  
Self Consistent ◽  
Small Wave ◽  
Many Body Perturbation Theory ◽  
Zero Frequency

The screening function of an interacting electron gas at high and metallic densities is investigated by many-body perturbation theory. The analysis is guided by a fundamental relation between the compressibility of the system and the zero-frequency small wave-vector screening function (i.e. screening constant). It is shown that the contribution from a graph not included in previous work is essential to obtain the lowest-order correlation correction to the screening constant at high density. Also, this graph gives a substantial contribution to the screening constant at metallic densities. The general problem of choosing a self-consistent set of graphs for calculating the screening function is discussed in terms of a coupled set of integral equations for the propagator, the self-energy, the vertex function, and the screening function. A modification of Hubbard's (1957) form of the screening function is put forward on the basis of these results.

THE PAIR DISTRIBUTION FUNCTION OF AN INTERACTING ELECTRON GAS

1967 ◽  
Vol 45 (9) ◽  
pp. 3139-3161 ◽  
Author(s):  
D. J. W. Geldart
Keyword(s):  
Distribution Function ◽  
Pair Distribution Function ◽  
Electron Gas ◽  
Pauli Principle ◽  
Distribution Functions ◽  
Upper And Lower Bounds ◽  
Wave Number ◽  
Many Body ◽  
Many Body Perturbation Theory ◽  
Simple Class

The pair distribution function, in the limit of zero separation, of an interacting electron gas at high and metallic densities is investigated by many-body perturbation theory. It is shown that the usual methods for maintaining self-consistency in approximate calculations violate, in general, the nonnegativity of the pair distribution function. In particular, the Pauli principle yields a rigorous sum rule for the parallel spin density fluctuation propagator which is not satisfied. Upper and lower bounds on one-loop and multiloop contributions to the pair distribution functions are given. These bounds are used to discuss correlation corrections. An improved wave-number dependence is given for Hubbard's (1957) approximation to the screening function and numerical results are given for a simple class of exchange corrections.

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