Localization properties of electronic wave functions of the Hubbard model on the Fibonacci lattice

We employ the Hubbard model on the Fibonacci lattice to study the effect of the repulsive Coulomb interaction on the electronic properties of quasicrystals. Localization properties of the electronic wave functions are analyzed numerically within the Hartree-Fock approximation. For the case when the Fermi energy locates in a gap, all the wave functions remain critical as indicated by a previous report. For the case when the Fermi energy lies on an accumulation point of the energy spectrum, the critical wave function is expected to be unstable because the self-consistent one-electron potential strongly breaks Conway's theorem on account of the long-range nature of the Friedel oscillation. Still, it is found that the critical nature remains stable provided the interaction is sufficiently weak. Instead, when the strength of the interaction is increased, the system becomes magnetically unstable much more easily than in the former case.