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

TL;DR

This study explores how electron-electron interactions induce magnetic states in a two-dimensional quasiperiodic tiling, revealing antiferromagnetic order and symmetry properties through numerical solutions of the Hubbard model.

Contribution

It provides the first detailed analysis of magnetic states in a 2D quasiperiodic tiling using the Hubbard model and Hartree-Fock approximation, highlighting inflation symmetry effects.

Findings

Antiferromagnetic order at half-filling

Magnetic configurations exhibit inflation symmetry

Local magnetization depends on local environments

Abstract

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 (Hubbard repulsion strength) 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 quasicrystal.