Cantor Spectra for Double Exchange Model

Details Cantor Spectra for Double Exchange Model Cantor Spectra for Double Exchange Model

2000-09-27

arxiv.org/abs/cond-mat/0009423v3

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 4 figures, revtex, corrected some typos, accepted for publication in PRB

Scientific paper

10.1103/PhysRevB.63.212403

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 $\alpha$'s are obtained. The energy spectrum is found to be a singular continuous, so-called the Cantor set with zero Lebesque measure.

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