Confined states in the tight-binding model on the hexagonal golden-mean tiling

Abstract

We study the tight-binding model with two distinct hoppings $(t_L,t_S)$ on the two-dimensional hexagonal golden-mean tiling and examine the confined states with $E=0$, where $E$ is the eigenenergy. Some confined states found in the case $t_L=t_S$ are exact eigenstates even for the system with $t_L\ne t_S$, where their amplitudes are smoothly changed. By contrast, the other states are no longer eigenstates of the system with $t_L\ne t_S$. This may imply the existence of macroscopically degenerate states which are characteristic of the system with $t_L=t_S$, and that a discontinuity appears in the number of the confined states in the thermodynamic limit.

7 pages, 5 figures

References in corpus (11)

• 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
• Non-Fermi-Liquid Behavior in Metallic Quasicrystals with Local Magnetic Moments
• 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
• Strictly localized states in the octagonal Ammann-Beenker quasicrystal
• 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 (3)

• Confined states and topological phases in two-dimensional quasicrystalline $\pi$-flux model
• Ferromagnetically ordered states in the Hubbard model on the $H_{00}$ hexagonal golden-mean tiling
• Modulated honeycomb lattices and their magnetic properties