论文标题
非热光谱的动物学及其图形拓扑
Zoology of non-Hermitian spectra and their graph topology
论文作者
论文摘要
我们揭示了通用有限的非铁谱的非常丰富的图形拓扑，该光谱与常规频带不变和复杂的光谱绕组不同。复杂光谱的图构型的特征是其相应能量分散的代数结构，在组合图理论，代数几何和非富甲虫带拓扑之间提出了新的紧密联系。共同相关的光谱图属于相同的等效类别，其特征是出现的对称性不一定存在于物理哈密顿量中。最简单的类包括众所周知的示例，例如Hatano-Nelson和非Hermitian SSH模型，而更复杂的类则代表具有相似恒星，花朵和昆虫的有趣光谱图的新型多组分模型。随着超级原子晶格和量子电路的最新快速发展，现在不仅可以在实验上实现这种深奥的光谱，而且还可以研究非弱的平坦频带和不同光谱图之间的异常反应。
We uncover the very rich graph topology of generic bounded non-Hermitian spectra, distinct from the topology of conventional band invariants and complex spectral winding. The graph configuration of complex spectra are characterized by the algebraic structures of their corresponding energy dispersions, drawing new intimate links between combinatorial graph theory, algebraic geometry and non-Hermitian band topology. Spectral graphs that are conformally related belong to the same equivalence class, and are characterized by emergent symmetries not necessarily present in the physical Hamiltonian. The simplest class encompasses well-known examples such as the Hatano-Nelson and non-Hermitian SSH models, while more sophisticated classes represent novel multi-component models with interesting spectral graphs resembling stars, flowers, and insects. With recent rapid advancements in metamaterials, ultracold atomic lattices and quantum circuits, it is now feasible to not only experimentally realize such esoteric spectra, but also investigate the non-Hermitian flat bands and anomalous responses straddling transitions between different spectral graph topologies.
