Hartree-Fock and random phase approximation theories in a many-fermion solvable model

We present an ideal system of interacting fermions where the solutions of the many-body Schrodinger 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.We present an ideal system of interacting fermions where the solutions of the many-body Schrodinger 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.303