非厄米量子非晶系统中的点隙拓扑
Point-gap topology in amorphous non-Hermitian quantum systems
AI总结：
针对非厄米非晶系统中谱不稳定导致难以识别拓扑边缘态的问题，建立稳定零模奇异态与隙间态的对应关系，基于哈密顿量奇异值分解构建实空间拓扑不变量，为点隙拓扑探索提供通用策略并重新定义非厄米皮效应。
AI中文摘要：
近期研究表明，在非厄米系统中，不仅谱绕数与皮模式的对应关系会失效，且其能谱对一般微扰、系统尺寸和边界条件高度敏感。在晶格位置不确定的非晶非厄米系统中，谱不稳定性更为严重，仅通过本征值谱难以识别稳定的拓扑边缘态。为应对这一挑战，我们建立了热力学极限下稳定零模奇异态与能谱中隙间态的对应关系。由于奇异值谱对微小微扰和尺寸变化具有高度鲁棒性，即使在有限尺寸系统中，也可通过奇异值可靠探测拓扑边缘态。基于哈密顿量的奇异值分解，我们在实空间构建拓扑不变量，以表征相关的拓扑保护边缘态。该方法为实空间中点隙拓扑的探索提供了通用策略，并从新视角重新定义了非厄米皮效应。
英文摘要：
Recent studies have revealed that not only does the correspondence between spectral winding numbers and skin modes break down in non-Hermitian systems, but the energy spectrum itself is highly sensitive to generic perturbations, system size, and boundary conditions. In amorphous non-Hermitian systems, where the positions of lattice sites are uncertain, the spectral instability becomes even more severe, making it difficult to identify stable topological edge states from the eigenvalue spectrum alone. To overcome this challenge, we introduce a correspondence between stable zero-mode singular states and mid-gap states of the energy spectrum in the thermodynamic limit. Because the singular value spectrum is highly robust against small perturbations and variation in size, topological edge states can be reliably probed via singular values even in finite-sized systems. Based on the singular-value decomposition of the Hamiltonian, we construct a topological invariant in real space to characterize the associated topologically protected edge states. Our approach provides a general strategy for exploring point-gap topology in real space and redefine the non-Hermitian skin effect from a new perspective.
