AN INTERPOLATING ANSATZ FOR THE GROUND-STATE OF THE SPINLESS FERMION HAMILTONIAN IN D=1 AND 2

We propose an interpolating ansatz between the strong coupling and wea k coupling regimes of a system of spinless interacting fermions in 1D and 2D lattices at half-filling. We address relevant issues such as th e existence of Long Range Order, quantum phase transitions and the eva luation of ground state energy. In 1D our method is capable of unveili ng 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 sta te energy. In 2D the van Hove singularity plays an essential role in c hanging the asymptotic behaviour of the system for large values of t/U . In particular, the staggered magnetization for large t/U does not di splay the Hartree-Fock law (t/U)e(-2 pi root t/U) but instead we find the law (t/U)e-(pi 2/3t/U). Moreover, the system does not exhibit bifu rcation phenomena and thus we do not find a critical point separating a CDW state from a fermion ''liquid'' state.