Ground State Properties of the Coupled Spin-Fermion Model in the Weak Kondo Coupling Region

Two dimensional coupled spin-fermion model as a model for high-T_c oxide is examined by using the perturbation method and the spin wave approximation in the weak Kondo coupling region. The logarithmic singularity appears in the fermion self energy. It is shown that one fermion doped into the Heisenberg spin system forms the self-trapped states of the fermion and spins. The doped many fermions remains localized as the self-trapped states below the critical fermion concentration. The relation to the Kondo effect is discussed. The relevance of our results to optical and photoemission experiments in high-T_c oxides is also discussed.