Topological Spectral Truncation in Non-Hermitian Chiral Graphs: Emergence of Discrete Frequency Locking

Abstract:We investigate the spectral properties of discrete non-Hermitian graphs endowed with local Z3 symmetry and chiral phase asymmetries. We introduce a Topological Spectral Truncation mechanism driven by the algebraic connectivity (Fiedler value) and its eigenvector perturbations. By rigorously diagonalizing the non-Hermitian Laplacian of chiral networks, we demonstrate two critical phenomena: 1) The system exhibits strict suppression of the non-Hermitian skin effect (NHSE), as confirmed by the exact overlap of open and periodic boundary spectra; 2) At a critical inter-cluster coupling strength (w = 0.121), the low-frequency eigenspectrum spontaneously yields a topologically protected frequency ratio of strictly 1 : 6.0 : 16.2. A random graph control fails to recover this ratio, proving its topological necessity. 摘要:我们研究了具有局域 Z3 对称性和手性相位不对称的离散非厄米图的谱特性。我们引入了一种由代数连通度(Fiedler值)及其特征向量微扰驱动的“拓扑谱截断”机制。通过对非厄米手性网络的严格对角化,我们展示了两个关键现象:1)系统表现出趋肤效应的严格抑制,这由开边界和周期边界谱的完美重合所证实;2)在临界簇间耦合强度(w = 0.121)下,低频本征谱自发涌现出被严格拓扑保护的 1 : 6.0 : 16.2 频率比例。随机图对照组完全无法重现该比例,证明了其拓扑必然性。