The book-keeping fermion analysis of the double exchange model with antiferromagnetic background

We analyze the double exchange model with antiferromagnetic background by the book-keeping fermion method. First, we consider the motion of a single conduction electron. We assume that the localized spins form the Néel state and the added conduction electron forms only three types of states under the strong Hund’s-rule coupling, and we regard these states as the book-keeping fermions. Under these assumptions, we first calculate the spectral functions and find a good agreement with the results given by the exact diagonalizations for finite-size clusters. We next consider the situation where there are finite numbers of spin flips occurring in the down-spin sublattice in the Néel ordered state. Considering the effects of the spin defects, we add a new book-keeping fermion and estimate the energy of the spin defects by a perturbation theory. This theory gives the phase diagram comparable with the numerical results.