Ferromagnetically ordered states in the Hubbard model on the $H_{00}$ hexagonal golden-mean tiling

TL;DR

This paper investigates magnetic properties of the Hubbard model on a quasiperiodic $H_{00}$ tiling, revealing ferromagnetic order in the weak coupling limit and analyzing magnetic crossover behavior.

Contribution

It provides an exact fraction of confined states using Lieb's theorem and demonstrates ferromagnetic order in a new quasiperiodic tiling, differing from known tilings.

Findings

Existence of extended states in one sublattice and confined states in the other.

Exact fraction of confined states is $1/2\tau^2$, with $\tau$ as the golden mean.

Ferromagnetic order appears in the weak coupling limit, with magnetic moments increasing with Coulomb interaction.

Abstract

We study magnetic properties of the half-filled Hubbard model on the two-dimensional $H_{00}$ hexagonal golden-mean quasiperiodic tiling. The tiling is composed of large and small hexagons, and parallelograms, and its vertex model is bipartite with a sublattice imbalance. The tight-binding model on the tiling has macroscopically degenerate states at $E = 0$. We find the existence of two extended states in one of the sublattices, in addition to confined states in the other. This property is distinct from that of the well-known two-dimensional quasiperiodic tilings such as the Penrose and Ammann-Beenker tilings. Applying the Lieb theorem to the Hubbard model on the tiling, we obtain the exact fraction of the confined states as $1/2\tau^2$, where $\tau$ is the golden mean. This leads to a ferromagnetically ordered state in the weak coupling limit. Increasing the Coulomb interaction, the staggered magnetic moments are induced and gradually increase. Crossover behaviour in the magnetically ordered states is also addressed in terms of perpendicular space analysis.