Antiferromagnetically ordered state in the half-filled Hubbard model on the Socolar dodecagonal tiling

TL;DR

This paper studies how antiferromagnetic order emerges in the half-filled Hubbard model on the Socolar dodecagonal tiling, revealing the role of degenerate states and local environments in magnetic properties.

Contribution

It demonstrates the emergence of antiferromagnetic order in a quasiperiodic tiling and compares magnetic properties across different tilings, highlighting the influence of local environments.

Findings

Sudden appearance of staggered magnetizations with interaction

Magnetization increases monotonically with interaction strength

Magnetization profiles vary with local environments

Abstract

We investigate the antiferromagnetically ordered state in the half-filled Hubbard model on the Socolar dodecagonal tiling. When the interaction is introduced, the staggered magnetizations suddenly appear, which results from the existence of the macroscopically degenerate states in the tightbinding model. The increase of the interaction strength monotonically increases the magnetizations although its magnitude depends on the local environments. Magnetization profile is discussed in the perpendicular space. The similarity and difference are also addressed in magnetic properties in the Hubbard model on the Penrose, Ammann-Beenker, and Socolar dodecagonal tilings.