An analytical method is presented that allows a unitary description of the Hubbard Hamiltonian with the Gutzwiller wave function, without the Gutzwiller approximation, in any dimension D. The method can also be extended for other Hamiltonians and wave functions.
A variational approach of the two-dimensional Hubbard model is presented, based on the Gutzwiller wave function, making no use of the Gutzwiller approximation. We calculated exactly the coefficients of the (g2-1)m expansion of the ground-state energy (g is the Gutzwiller variational parameter) up to the m=8 order. The m>8 terms were deduced with an acuracy O[(n/2)18] as a function of the electron concentration n. Double occupancy, expectation value of the interaction energy, average kinetic energy, and the minimized ground-state energy are determined and their electron concentration and dimensionality dependence are discussed. An evaluation of the nonanalyticities for any dimension is also presented.