Related papers: Analytical solution of open crystalline linear 1D …
Finite topologically non-trivial systems are often characterised by the presence of bound states at their physical edges. These topological edge modes can be distinguished from usual Shockley waves energetically, as their energies remain…
The one-dimensional Hubbard model with open boundary conditions is exactly solved by means of algebraic Bethe ansatz. The eigenvalue of the transfer matrix, the energy spectrum as well as the Bethe ansatz equations are obtained.
For a wide class of noninteracting tight-binding models in one dimension we present an analytical solution for all scattering and edge states on a half-infinite system. Without assuming any symmetry constraints we consider models with…
We use the Bethe Ansatz solution for the one dimensional Hubbard model with open boundary conditions and applied boundary fields to study the spectrum of bound states at the boundary. Depending on the strength of the boundary potentials one…
We present a numerical method which accurately computes the discrete spectrum and associated bound states of Hamiltonians which model electronic "edge" states localized at boundaries of one and two-dimensional crystalline materials. The…
Based on a recent generalization of Bloch's theorem, we present a Bloch ansatz for the Harper model with an arbitrary rational magnetic flux in various geometries, and solve the associated ansatz equations analytically. In the case of a…
We present a quantitative analysis of two-particle interaction effects in generalized, one-dimensional Aubry-Andr\'e-Harper models with the Fermi energy placed in one of the band gaps. We investigate systems with periodic as well as open…
Atomic-scale helices exist as motifs for several material lattices. We examine a tight-binding model for a single one-dimensional monatomic chain with a p-orbital basis coiled into a helix. A topologically nontrivial phase emerging from…
The bulk boundary correspondence, one of the most significant features of topological matter, theoretically connects the existence of edge modes at the boundary with topological invariants of the bulk spectral bands. However, it remains…
We study the eigenspectrum properties of a one-dimensional molecular chain composed of hexagonal unit cells. The system features two alternating hopping parameters, resulting in a rich energy spectrum with both dispersive and flat bands. By…
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…
We propose a systematic analysis of the eigenfunctions of two-band systems in two dimensions with a circular edge. Our approach is based on an analytic continuation of the wavenumber, which yields a mapping from the bulk modes to the edge…
We propose a novel and systematic recurrence method for the energy spectra of non-Hermitian systems under open boundary conditions based on the recurrence relations of their characteristic polynomials. Our formalism exhibits better accuracy…
Methods for calculating lower bounds to the exact energy using the variance of the upper bound energy are discussed and explored. All the matrix elements of the Hamiltonian squared are collected and considered, and those for which no known…
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 investigate the edge state of a two-dimensional topological insulator based on the Kane-Mele model. Using complex wave numbers of the Bloch wave function, we derive an analytical expression for the edge state localized near the edge of a…
A simple picture for the spectrum of the one-dimensional Hubbard model is presented using a classification of the eigenstates based on an intuitive bound-state Bethe-Ansatz approach. This approach allows us to prove a "string hypothesis"…
We investigate the topology of the different phases of the extended Su-Schrieffer-Heeger (eSSH) model, which includes hopping processes between translationally inequivalent atoms beyond nearest neighbors. Exact analytical expressions for…
The energy bands of non-Hermitian systems exhibit nontrivial topological features that arise from the complex nature of the energy spectrum. Under periodic boundary conditions (PBC), the energy spectrum describes rather generally closed…
Motivated by the challenge of seeking a rigorous foundation for the bulk-boundary correspondence for free fermions, we introduce an algorithm for determining exactly the spectrum and a generalized-eigenvector basis of a class of banded…