AI 中文总结
该研究推导了非厄米晶格系统中依赖动量的相似变换保持体谱的条件，明确变换坐标下的体拓扑不变量可可靠预测边界物理，为相关领域提供了关键理论依据。
AI 中文摘要
我们研究依赖动量的相似变换保持具有开放边界条件（OBC）的晶格哈密顿量谱性质的条件。这类变换在无限系统中可精确保持谱，但应用于有限系统时，因实空间中逆变换的长程特性会引入微妙问题。针对一般无迹2×2哈密顿量，我们推导了通过常数相似变换约化为斜对角形式的充要条件，为所有情况提供了显式变换矩阵。随后，我们确立了依赖动量的变换下体谱保持的严格条件：H的广义布里渊区必须位于det S(z)的最小零点内（双半径条件rGBZ^max < z_min），同时对H有谱稳定性（无临界非厄米皮肤效应）条件。S(z)的双侧性仅影响有限个边界本征值，不影响体。我们的结果明确了在变换坐标中计算的体拓扑不变量何时能可靠预测边界物理，对非厄米系统、光子晶体及其他仅在适当基矢变换后出现手征或隐藏对称性的平台具有重要意义。
英文摘要
We investigate the conditions under which momentum-dependent similarity transformations preserve spectral properties of lattice Hamiltonians with open boundary conditions (OBC). While such transformations exactly preserve spectra in infinite systems, their application to finite systems introduces subtleties due to the long-range nature of the inverse transformation in real space. For general traceless $2\times 2$ Hamiltonians, we derive necessary and sufficient conditions for reduction to skew-diagonal form via constant similarity transforms, providing explicit transformation matrices for all cases. We then establish rigorous conditions for bulk spectral preservation under momentum-dependent transformations: the generalized Brillouin zone of $H$ must lie inside the smallest zero of $\det S(z)$ (the two-radius condition $r_{\mathrm{GBZ}}^{\max}<z_{\min}$), together with a spectral-stability (no critical non-Hermitian skin effect) condition on $H$. Two-sidedness of $S(z)$ governs only the modification of a finite number of boundary eigenvalues, not the bulk. Our results establish when bulk topological invariants computed in transformed coordinates reliably predict boundary physics, with implications for non-Hermitian systems, photonic crystals, and other platforms where chiral or hidden symmetries emerge only after appropriate basis changes.
