Density-of-states and localization study of the double-exchange model in one and two dimensions

We have studied the density-of-states and localization properties of the double-exchange (DE) model in one and two dimensions to see how it is influenced by the complex phase of the hopping matrix elements. This has been done by comparing exact results in finite-size systems for the DE model with complex phase, without it (|DE|), and for a bond-disorder model with a rectangular distribution of hopping matrix elements. Localization properties have been investigated by calculating the participation number. We have found that, although all states are localized away from the band center, there exists an energy range about the band center within which the complex phase tends to reduce the degree of localization of the eigenstates, while outside of this energy range it tends to further localize them. The DE and |DE| models exhibit critical behavior in a wide energy range around band center where the localization length is much larger than the system sizes studied here. All three models exhibit critical behavior at the band center with scaling properties changing discontinuously as function of energy at $E=0.\mathrm{}$ We interpret this as a sign of criticality of the band center state at all length scales.