Exact solutions of non-Hermitian chains with asymmetric long-range hopping under specific boundary conditions

• 作者: Cui-Xian Guo Shu Chen
• 来源期刊: 中国物理B（英文版）
• 年，卷（期）: 2022,（1）
• 所属期刊栏目: SPECIAL TOPIC— Non-Hermitian physics
• 页码范围: 92-98
• 页数: 7页
• 语种: 英文
• DOI: 10.1088/1674-1056/ac3228

摘要

We study the one-dimensional general non-Hermitian models with asymmetric long-range hopping and explore how 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 those of the periodical system when the hopping parameters fulfill certain conditions,whereas the eigenstates display the non-Hermitian skin effect.