Cantor Spectra for Double Exchange Model

Abstract

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