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

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.

11 pages, 14 figures

References in corpus (12)

• Quantum critical state in a magnetic quasicrystal
• Superconductivity on a Quasiperiodic Lattice: Extended-to-Localized Crossover of Cooper Pairs
• Antiferromagnetic order in the Hubbard Model on the Penrose Lattice
• Conventional superconductivity in quasicrystals
• Non-Fermi-Liquid Behavior in Metallic Quasicrystals with Local Magnetic Moments
• Physical properties of weak-coupling quasiperiodic superconductors
• Superlattice structure in the antiferromagnetically ordered state in the Hubbard model on the Ammann-Beenker tiling
• Valence Fluctuations and Electric Reconstruction in the Extended Anderson Model on the Two-Dimensional Penrose Lattice
• Local Electron Correlations in a Two-dimensional Hubbard Model on the Penrose Lattice
• Distributed Hybridization Model for Quantum Critical Behavior in Magnetic Quasicrystals
• Ferrimagnetically ordered states in the Hubbard model on the hexagonal golden-mean tiling
• Antiferromagnetically ordered state in the half-filled Hubbard model on the Socolar dodecagonal tiling

Cited by in corpus (4)

• Hyperuniform properties of the square-triangle tilings
• Gapless superconductivity and its real-space topology in quasicrystals
• Brillouin zone folding method for quasiperiodic superconductivity in multilayer systems: application to electronic structure and optical responses
• Modulated honeycomb lattices and their magnetic properties