Exactly Solvable Model Systems and the Hartree-Fock-Bogolubov Approximation for Model Systems with Four-Fermion Interaction

George P. Flessas

S. J. Krieger

Nikolay N. Bogolubov, Andrey Vladimirovich Soldatov

An approach is proposed which allows one to investigate dynamical and thermodynamical properties of models with four-fermion interaction of general type. The approach combines ideas of the standard Bogolubov's approximating Hamiltonian method for the models with separable interaction with the method of Hartree–Fock approximation based on the ideas of self-consistency.

M. C. Cambiaggio, Angel Ricardo Plastino, L. Szybisz

Fabrizio Tafuri, C. A. Perroni, G. De Filippis

Giampaolo Co', Stefano De Leo

We present an ideal system of interacting fermions where the solutions of the many-body Schrödinger equation can be obtained without making approximations. These exact solutions are used to test the validity of two many-body effective approaches, the Hartree–Fock and the random phase approximation theories. The description of the ground state done by the effective theories improves with increasing number of particles.