EXACT WAVEFUNCTION OF THE ONE-DIMENSIONAL DOUBLE-EXCHANGE MODEL WITH ONE ELECTRON

We study the one-dimensional double-exchange model with L localized spins and one mobile electron. We solve the Schrodinger equation analytically and obtain the energies and wavefunctions for all the eigenstates with spin S = (l - 1)/2 exactly. As an application, we compute the single-particle Green's function. We show that, for vanishing exchange interactions between localized spins, the single-particle spectrum is entirely incoherent and the lowest band has an infinite band mass, i.e., the single electron is localized due to its interaction with the spin excitations. For nonvanishing exchange interactions between localized spins, the lower edge of the spectrum acquires a dispersion but the spectrum remains incoherent with no well-defined quasiparticle peak.