Magnetic states induced by electron-electron interactions in a plane quasiperiodic tiling

We consider the Hubbard model for electrons in a two-dimensional quasiperiodic tiling using the Hartree–Fock approximation. Numerical solutions are obtained for the first three square approximants of the perfect octagonal tiling. At half-filling, the magnetic state is antiferromagnetic. We calculate the distributions of local magnetizations and their dependence on the local environments as U is varied. The inflation symmetry of quasicrystals results in a corresponding inflation symmetry of the magnetic configurations when passing from one tiling to the next in the progression towards the infinite