相关论文: Exact Eigenstates of Tight-Binding Hamiltonians on…
Analytic and numerical results for quasiperiodic tight-binding models are reviewed, with emphasis on two and three-dimensional models which so far are beyond a mathematically rigorous treatment. In particular, we consider energy spectra of…
We present exact solutions for some eigenstates of hopping models on one and two dimensional quasiperiodic tilings and show that they are "critical" states, by explicitly computing their multifractal spectra. These eigenstates are shown to…
The eigenstates of d-dimensional quasicrystalline models with a separable Hamiltonian are studied within the tight-binding model. The approach is based on mathematical sequences, constructed by an inflation rule P = {w -> s, s -> sws^(b-1)}…
We study electronic eigenstates on quasiperiodic lattices using a tight-binding Hamiltonian in the vertex model. In particular, the two-dimensional Penrose tiling and the three-dimensional icosahedral Ammann-Kramer tiling are considered.…
One of the most used approaches in simulating materials is the tight-binding approximation. When using this method in a material simulation, it is necessary to compute the eigenvalues and eigenvectors of the Hamiltonian describing the…
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…
It is shown that, an entire class of off-diagonally disordered linear lattices composed of two basic building blocks and described within a tight binding model can be tailored to generate absolutely continuous energy bands. It can be…
An investigation on the properties of electronic states of a tight-binding Hamiltonian on the Apollonian network is presented. This structure, which is defined based on the Apollonian packing problem, has been explored both as a complex…
We find novel confined states in the spin-$S$ nearest-neighbor antiferromagnetic Heisenberg model on the two-dimensional Penrose lattice. Linear spin waves have massively degenerate eigenstates strictly confined to tricoordinated sites.…
We show that, under certain combinations of the parameters governing the interaction of a harmonically trapped ion with a laser beam, it is possible to find one or more exact eigenstates of the Hamiltonian, with no approximations except the…
Finite strips, composed of a periodic stacking of infinite quasiperiodic Fibonacci chains, have been investigated in terms of their electronic properties. The system is described by a tight binding Hamiltonian. The eigenvalue spectrum of…
We present a scheme to controllably improve the accuracy of tight-binding Hamiltonian matrices derived by projecting the solutions of plane-wave ab initio calculations on atomic orbital basis sets. By systematically increasing the…
We propose an ansatz for the wave function of a non-interacting quantum particle in a deterministic quasicrystalline potential. It is applicable to both continuous and discrete models and includes Sutherland's hierarchical wave function as…
Analytic technique based on Chebyshev polynomials is developed for studying two-dimensional lattice ribbons with hopping anisotropy. In particular, the tight-binding models on square and triangle lattice ribbons are investigated with…
We propose a new example of discrete holography that provides a new step towards establishing the AdS/CFT duality for discrete spaces. A class of boundary Hamiltonians is obtained in a natural way from regular tilings of the hyperbolic…
We present an accurate ab initio tight-binding model, capable of describing the dynamics of Dirac points in tunable honeycomb optical lattices following a recent experimental realization [L. Tarruell et al., Nature 483, 302 (2012)]. Our…
In this article we prove that a large class of inflation tilings are hyperuniform: this includes the novel hat tilings introduced by Smith et al. and well known examples such as Penrose, Ammann-Beenker and shield tilings. In some cases,…
We consider a model proposed before for a time-reversal-invariant topological superconductor (TRITOPS) which contains a hopping term $t$, a chemical potential $\mu$, an extended $s$-wave pairing $\Delta$ and spin-orbit coupling $\lambda$.…
We present a new model describing strongly correlated electrons on a general $d$-dimensional lattice. It differs from the Hubbard model by interactions of nearest neighbours, and it contains the $t$-$J$ model as a special case. The model…
Harrison's tight-binding theory provides an excellent qualitative description of the electronic structure of the elements across the periodic table. However, the resulting band structures are in significant disagreement with those found by…