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.
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