Cantor spectra for the double-exchange model

We numerically study energy spectra and localization properties of the double-exchange model at an irrational filling factor. For systematic finite-size scaling analysis, we use a numerical technique in momentum space by an ``embedded'' boundary condition that has no finite-size effect a priori. Although the Hamiltonian has translation invariance, the ground state spontaneously exhibits a self-similarity. Scaling and multifractal analysis for the wave functions are performed and the scaling index α's are obtained. The energy spectrum is found to be singular, continuous, the so-called Cantor set with zero Lebesque measure.