It is a well known fact that mean-field approximation to the nuclear many-body problem introduces center-of-mass (CM) spurious components in the solutions. In particular, Hartree-Fock self-consistent mean-fields obtained using realistic forces in a non-relativistic approach have been considered, and the corresponding CM corrections have been calculated for the energy [1, 2] as well as for other...

This article is concerned with the derivation and the mathematical study of a new mean-field model for the description of interacting electrons in crystals with local defects. We work with a reduced Hartree-Fock model, obtained from the usual Hartree-Fock model by neglecting the exchange term. First, we recall the definition of the self-consistent Fermi sea of the perfect crystal, which is obta...

In this paper, we investigate the ϕ4 model with cutoffs. By introducing a spatial cutoff and momentum cutoff, total Hamiltonian is self-adjoint operator on boson Fock space. Under regularity conditions of obtain first order expansion non-degenerate ground state energy Hamiltonian.

We study the homogeneous interacting hole gas in p-doped bulk III-V semiconductors. The structure of the valence band is modeled by Luttinger’s Hamiltonian in the spherical approximation, giving rise to heavy and light hole dispersion branches, and the Coulomb repulsion is taken into account via a self-consistent HartreeFock treatment. As a nontrivial feature of the model, the self-consistent s...

In this article, we set up a functional setting for mean-field electronic structure models of Hartree-Fock or Kohn-Sham types for disordered crystals. The electrons are quantum particles and the nuclei are classical point-like particles whose positions and charges are random. We prove the existence of a minimizer of the energy per unit volume and the uniqueness of the ground state density of su...

Based on Pulay's direct inversion iterative subspace (DIIS) approach, we present a method to accelerate self-consistent field (SCF) convergence. In this method, the quadratic augmented Roothaan-Hall (ARH) energy function, proposed recently by Høst and co-workers [J. Chem. Phys. 129, 124106 (2008)], is used as the object of minimization for obtaining the linear coefficients of Fock matrices with...

We discuss two different approximation schemes for the self-consistent solution of the relativistic Brueckner-Hartree-Fock equation for finite nuclei. In the first scheme, the Dirac effects are deduced from corresponding nuclear matter calculations, whereas in the second approach the local-density approximation is used to account for the effects of correlations. The results obtained by the two ...

This paper is concerned with the well-posedness analysis of the Hartree-Fock system modeling the time evolution of a quantum system comprised of fermions. We consider quantum states with finite mass and finite kinetic energy, and the self-consistent potential is the unbounded Coulomb interaction. This model is first formulated as a semi-linear evolution problem for the one-particle density matr...

The isotropic Compton profile of lithium fluoride has been deduced from Compton scattering measurements on poly crystalline sample at gamma ray source energy of 662 keV. Here we report the experimental and theoretical Compton profile of lithium fluoride. We calculated directional Compton profile and their anisotropic effect using self-consistent Hatree-Fock wave functions employed on the linear...

We investigate the effect of uniaxial heterostrain on interacting phase diagram magic-angle twisted bilayer graphene. Using both self-consistent Hartree-Fock and density-matrix renormalization group calculations, we find that small strain values (??0.1%–0.2%) drive a zero-temperature transition between symmetry-broken “Kramers intervalley-coherent” insulator nematic semimetal. The critical lies...