On the Ground State of B.C.C. 3He

1972 ◽  
Vol 50 (11) ◽  
pp. 1143-1151 ◽  
Author(s):  
H. R. Glyde ◽  
F. C. Khanna
Keyword(s):  
Single Particle ◽  
Ground State ◽  
State Energy ◽  
Solid Helium ◽  
Lattice Dynamic ◽  
Matrix Approximation ◽  
Hartree Fock ◽  
Volume Dependence ◽  
T Matrix ◽  
Good Agreement

The ground state properties of b.c.c. 3He are computed using both the localized single particle functions due to Nosanow and the correlated functions due to Koehler in conjunction with the T-matrix approximation of Glyde and Khanna. The trial functions and T matrix are computed iteratively much as suggested for the Brueckner–Hartree–Fock scheme for nuclear matter. The correlated ground state energy lies ~6 cal/mole below the single particle value and is in good agreement with the observed value of Pandorf and Edwards. The volume dependence, however, is poor suggesting that cubic terms such as incorporated in the improved theory of Goldman et al. are important in solid helium. When combined with lattice dynamic work, the present results suggest correlated functions provide a much better description of solid helium.

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.

An Interpolating Ansatz for the Ground State of the Spinless Fermion Hamiltonian in D=1 and 2

1997 ◽  
Vol 11 (13) ◽  
pp. 1545-1563
Author(s):  
Miguel A. Martín-Delgado ◽  
Germán Sierra
Keyword(s):  
Critical Point ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Quantum Phase Transitions ◽  
Hartree Fock ◽  
Spinless Fermion ◽  
A Value ◽  
Bifurcation Phenomena ◽  
Half Filling

We propose an interpolating ansatz between the strong coupling and weak coupling regimes of a system of spinless interacting fermions in 1D and 2D lattices at half-filling. We address relevant issues such as the existence of Long Range Order, quantum phase transitions and the evaluation of ground state energy. In 1D our method is capable of unveiling the existence of a critical point in the coupling constant at (t/U) c =0.7483 as in fact occurs in the exact solution at a value of 0.5. In our approach this phase transition is described as an example of Bifurcation Phenomena in the variational computation of the ground state energy. In 2D the van Hove singularity plays an essential role in changing the asymptotic behaviour of the system for large values of t/U. In particular, the staggered magnetization for large t/U does not display the Hartree–Fock law [Formula: see text] but instead we find the law [Formula: see text]. Moreover, the system does not exhibit bifurcation phenomena and thus we do not find a critical point separating a CDW state from a fermion "liquid" state.

scholarly journals HARTREE–FOCK GROUND STATE OF THE COMPOSITE FERMION METAL

1995 ◽  
Vol 09 (14) ◽  
pp. 889-894
Author(s):  
PIOTR SITKO ◽  
LUCJAN JACAK
Keyword(s):  
Single Particle ◽  
Ground State ◽  
Particle Energy ◽  
Fermi Velocity ◽  
Exchange Term ◽  
Single Particle Energy ◽  
Composite Fermion ◽  
Hartree Fock ◽  
Logarithmic Interaction ◽  
Particle Exchange

Within the Hartree–Fock approximation the ground state of the composite fermion metal is found. We observe that the single-particle energy spectrum is dominated by the logarithmic interaction exchange term which leads to an infinite jump of the single-particle exchange at the Fermi momentum. It is shown that the Hartree–Fock result brings no corrections to the RPA Fermi velocity.

scholarly journals Ground state calculations of the confined molecular ions H2+ and HeH++ using variational Monte Carlo method

2016 ◽  
Vol 94 (5) ◽  
pp. 501-506 ◽  
Author(s):  
Salah B. Doma ◽  
Fatma N. El-Gammal ◽  
Asmaa A. Amer
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Ground State ◽  
State Energy ◽  
Molecular Ions ◽  
Variational Monte Carlo ◽  
Molecular Ion ◽  
Spheroidal Cavity ◽  
Variational Monte Carlo Method ◽  
Good Agreement

The ground state energy of hydrogen molecular ion [Formula: see text] confined by a hard prolate spheroidal cavity is calculated. The case in which the nuclear positions are clamped at the foci is considered. Our calculations are based on using the variational Monte Carlo method with an accurate trial wave function depending on many variational parameters. The results were extended to also include the HeH++ molecular ion. The obtained results are in good agreement with the most recent results.

On the Ground State of H-

1981 ◽  
Vol 36 (7) ◽  
pp. 782
Author(s):  
Uday Vanu Das Gupta ◽  
Subal Chandra Saha ◽  
Sankar Sengupta
Keyword(s):  
Oscillator Strength ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Expectation Values ◽  
Hartree Fock ◽  
Present Procedure

Abstract A simple and effective method is described to calculate the ground state energy of H~ starting with the Hartree Fock wavefunction. The expectation values of the opera­ tors 〈r1 • r2〉, 〈r1n + r2n〉 and 〈p1 • p2〉 can be estimated easily with the present procedure. Oscillator strength sums S(k) for k= -1,0, 1 are also evaluated.

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