AI 中文总结
研究长程耦合系统中计算能带结构的两种方法，通过一维量子发射链在自由空间及与波导耦合情况对比，发现周期性边界条件结果更稳健，无限链方法有问题，且波导系统有非星形广义布里渊区等异常，解释了非厄米趋肤效应。
AI 中文摘要
为实现晶格模型能带结构计算的平移对称性，可考虑无限晶格或施加周期性边界条件。在短程耦合系统中这两种方法等效，但长程耦合时结果差异大。本文在一维量子发射链中比较这两种方法，链处于自由空间及与波导耦合时。后者允许非对称耦合产生非厄米趋肤效应，用两种能带结构计算方法分析。发现仅周期性边界条件能得到物理和数学上稳健的结果，无限链方法存在收敛问题且无法合理解释波导系统中非厄米趋肤效应的出现。此外，波导系统有非星形广义布里渊区和零缠绕数的强局域本征态等异常发现。
英文摘要
To achieve translational symmetry for the computation of the band structure of a lattice model, one can either consider an infinite lattice or impose periodic boundary conditions (PBC). While in systems with short-range couplings these two approaches are equivalent, we show that for long-range couplings one can obtain considerably different results. We compare the two methods on the basis of one-dimensional quantum emitter chains both in free space and when coupled to a waveguide. The latter system allows for asymmetric couplings enabling the non-Hermitian skin effect, which we analyze using the two different band-structure calculation methods. We find that only PBC lead to physically and mathematically robust results, while the infinite-chain approach entails convergence issues and is unable to satisfyingly explain the emergence of the non-Hermitian skin effect in the waveguide system. Using PBC reveals unusual findings like a non-star shaped generalized Brillouin zone and strongly localized eigenstates with zero winding number.
Comments15 pages, 9 figures
