Fixed Point of the Spin-Fermion Model Doped with a Single Fermion

Spin-fermion model on a square lattice is investigated in the perturbation expansion in terms of the spin-fermion Kondo coupling. The fermion self-energy is calculated in a selfconsistent treatment by a dominant pole approximation. The quasi-particle excitation of a doped fermion turns out to be totally incoherent. It suggests that the low energy excitations should be described by the bound state of a fermion and spins as a collective mode and imply that the fixed point of the spin-fermion model with a single fermion is the t-J model. It also suggests the spin-charge separation of the low energy excitations in the light doping region of these two models.