  We theoretically study the effect of electron-electron interactions on the
metallic state of quasicrystals. To address the problem, we introduce the
extended Hubbard model on the Ammann-Beenker tiling as a simple theoretical
model. The model is numerically solved within an inhomogeneous mean-field
theory. Because of the lack of periodicity, the metallic state is nonuniform in
the electron density even in the noninteracting limit. We clarify how this
charge distribution pattern changes with electron-electron interactions. We
find that the intersite interactions change the distribution substantially and
in an electron-hole asymmetric way. We clarify the origin of these changes
through the analyses in the real and perpendicular spaces. Our results offer a
fundamental basis to understand the electronic states in quasicrystalline
metals.
