AI 中文总结
本文研究带次近邻相互作用与平衡损耗-增益的非厄米SSH型三聚体模型，确立其在不同边界条件下的平带、体-边界对应关系及非厄米皮肤效应，解析推导相关本征态与拓扑不变量。
AI 中文摘要
我们考虑具有次近邻（NNN）相互作用和平衡损耗-增益（BLG）的Su-Schrieffer-Heeger（SSH）型三聚体模型，以研究晶格对称性、拓扑、非厄米性和一般边界条件（GBC）对平带存在性及体-边界对应关系（BBC）性质的综合影响。我们推导了周期边界条件（PBC）下完全实谱存在的充要条件，解析得到了PBC下对应平带的紧束缚态（CLS）和能量本征值的精确表达式。通过分别计算Zak相位和子晶格Zak相位，确立了PT对称性和赝手性对称性下的拓扑相变（TPT）。数值研究了开放边界条件（OBC）下的哈密顿量，在拓扑非平凡相中观测到边缘态，从而确立了非厄米BBC。对于仅具有赝手性对称性的系统，CLS存在于体相和边界；额外的PT对称性会破坏边界处的CLS。我们推广了已知形式主义，以研究同一哈密顿量在GBC下的情况，在PBC下允许平带的参数范围内，解析推导了一类边界条件下的能量和本征态表达式。在拓扑非平凡相中，解析得到了包括OBC在内的这些边界条件下的边缘态，从而确立了BBC。在具有互易体相互作用和强非互易边界项的模型中观测到了非厄米皮肤效应（NHSE），并解析计算了基于谱拓扑的绕数。
英文摘要
We consider a Su-Schrieffer-Heeger(SSH)-type trimer model with next-nearest-neighbor(NNN) interaction and balanced loss-gain(BLG) to study the combined effect of lattice symmetries, topology, non-hermiticity and general boundary conditions(GBC)on the existence of flat band and the nature of Bulk-Boundary correspondence(BBC). We derive the necessary and sufficient conditions for the existence of an entirely real spectrum under the periodic boundary condition(PBC). The exact expressions for the compact localized states(CLS) and energy eigenvalues corresponding to flat bands are derived analytically under the PBC. We establish topological phase transitions(TPT) for PT-symmetry and pseudo-chiral symmetry through the computation of the Zak phase and sub-lattice Zak phase, respectively. The Hamiltonian under the open boundary condition(OBC) is studied numerically, and edge states are observed in the topologically non-trivial phase, thereby establishing the non-hermitian BBC. The CLS exists in both bulk and the boundary for systems having only pseudo-chiral symmetry, and an additional PT-symmetry destroys the CLS at the boundary. We generalize a known formalism to study the same Hamiltonian under GBC, and derive analytic expressions for the energy and eigenstates for a class of boundary conditions in parametric ranges which admit flat band under the PBC. The edge states for these boundary conditions, including the OBC, are obtained analytically in the topologically non-trivial phase, thereby establishing BBC. The non-hermitian skin effect(NHSE) is seen in the model with reciprocal bulk interaction and strongly non-reciprocal boundary terms. The winding number based on spectral topology is computed analytically.
Comments24 pages, 11 figures, two columns
