SINGLE SPIN FLIP IN THE INFINITE U HUBBARD MODEL: HUBBARD OPERATORS, THREE-BODY FADEEV EQUATIONS AND GUTZWILLER WAVE FUNCTIONS

Abstract

We investigate a recently proposed many-body theory for composite (Hubbard) operators (A.E. Ruckenstein and S. Schmitt-Rink, Phys. Rev. B38, 7188 (1988)) in the context of the problem of a single spin flip in the saturated ferromagnetic state of the infinite U Hubbard model. We prove that the suitably defined strong coupling Hartree-Fock mean field theory leads to results identical to those obtained from the Gutzwiller wave function through exact evaluation of the kinetic energy. Most interestingly, we also show how exactly the same results can be obtained starting from the weak coupling limit by solving analytically the three-body t-matrix (Fadeev) equations in the infinite U limit. This work also sheds light on the physical content of slave boson approximations to which our approach was previously shown to be equivalent in the limit of large spin or orbital degeneracy. For the single spin flip problem we compare our results with those obtained by Bethe-Goldstone perturbation theory, Bethe Ansatz in one dimension, and exact diagonalization studies.