Directed polymers in Hartree-Fock approximation

Michele Fabrizio

Claude Aslangul, Daniel Saint-James

We establish the continuum version for the model of 1-d organic polymers by taking into account within a SSH type formulation the lattice deformation, and within a Hubbard interaction, the electronic correlation. The deduced Hamiltonian belongs to the category of field theories with internal symmetry. We treat it by a self-consistent field method and we obtain in a simple way the results already deduced by direct calculation on the lattice model. This allows for a discussion of the validity of continuum models.

Nathan E. Brener, John L. Fry

In this paper we derive a formula for the time-dependent Hartree-Fock dielectric function by using Green's-function theory. We develop a set of self-consistent equations for the self energy, polarization, and Green's function which can be iterated to obtain successively more accurate approximations for the polarization. In this procedure the Hartree and Hartree-Fock approximations occur naturally as the first and second steps in the iterations. As the iterations are carried out, we obtain not only the expressions for the polarization, but also the one-electron Hartree-Fock equations, so that there is no question as to which polarization formula corresponds to which equation. In this way we obtain an expression for the dielectric function which clearly and directly corresponds to the Hartree-Fock equation and which is therefore called the time-dependent Hartree-Fock (TDHF) dielectric function. In this TDHF formula for the dielectric function, the first term is the time-dependent Hartree or random-phase approximation dielectric function. We show that in order to be consistent with the theory, one should use Hartree wave functions and energies to compute random-phase approximation dielectric functions and Hartree-Fock wave functions and energies to compute TDHF dielectric functions. Numerical results are presented for the free-electron gas.

Stella M. Peltier, A. Piastino

Guillermo H. Bozzolo, James P. Vary, N. Canosa +2 more

Pan Zhang

The occupation renormalized Hartree-Fock single particle potential is extended to include the 'particle' state occupation. The exact solution, the solution of the occupation renormalized Hartree-Fock approximation and that of the Hartree-Fock approximation are calculated in Lipkin Model. It turns out that the RHF solution is more close to the exact one than the HF solution. The effect of occupation probability depends on the strength of the interaction of the two body term.