Exact solutions of non-Hermitian chains with asymmetric long-range hopping under specific boundary conditions
arXiv:2201.12613 · doi:10.1088/1674-1056/ac3228
Abstract
We study one-dimensional general non-Hermitian models with asymmetric long-range hopping and explore to analytically solve the systems under some specific boundary conditions. Although the introduction of long-range hopping terms prevents us from finding analytical solutions for arbitrary boundary parameters, we identify the existence of exact solutions when the boundary parameters fulfill some constraint relations, which give the specific boundary conditions. Our analytical results show that the wave functions take simple forms and are independent of hopping range, while the eigenvalue spectra display rich model-dependent structures. Particularly, we find the existence of a special point coined as pseudo-periodic boundary condition, for which the eigenvalues are the same as the periodical system when the hopping parameters fulfill certain conditions, whereas eigenstates display non-Hermitian skin effect.
7 pages, 4 figures
References in corpus (6)
- Topological Origin of Non-Hermitian Skin Effects
- Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
- Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
- Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
- Non-Bloch topological invariants in a non-Hermitian domain-wall system
- Exact solution of single impurity problem in non-reciprocal lattices: impurity induced size-dependent non-Hermitian skin effect