非厄米晶格中体态密度的普适性
Universal aspects of bulk density of states in non-Hermitian lattices
AI总结：
该研究证明非厄米晶格体态密度的表观歧义是虚幻的，确立了有限范围紧束缚哈密顿量的普适体态结构，确定布朗测度为规范体态DOS，还给出点隙拓扑相关的普适约束与本征值积累判据。
AI中文摘要：
非厄米晶格哈密顿量通常表现出强边界敏感性，周期边界条件与开放边界条件会在复能平面上产生截然不同的态密度（DOS）。这使得学界普遍认为，扩展非厄米系统缺乏唯一的体态DOS，不同的处理方案对应不等价的体态物理。本文证明，这种表观歧义在很大程度上是虚幻的。对于任何有限范围的紧束缚哈密顿量，我们确立了一种普适的体态结构：所有作为有限系统热力学极限得到的DOS定义，具有相同的多极矩，且在有限时间内、在远离边界处测量的可观测量会产生相同的体态动力学。这种普适性与热力学格林函数密切相关，我们证明，对于足够大的复频率，格林函数与边界条件无关。在所有等价描述中，我们确定通过厄米化与预解式分析得到的布朗测度是体态DOS的规范且便捷的代表，可直接从无限体积哈密顿量定义。我们进一步证明，点隙拓扑施加了额外的普适约束：边界依赖的格林函数在拓扑平凡的点隙中必须完全重合。这尤其提供了一种适用于任意维度的系统的系统判据，用于确定不同边界截断的本征值在复平面上的何处、以何种方式积累，并精确界定DOS歧义具有物理意义的范围。
英文摘要：
Non-Hermitian lattice Hamiltonians generally exhibit strong boundary sensitivity, with periodic and open boundary conditions producing distinct density of states (DOS) in the complex-energy plane. This has led to the view that extended non-Hermitian systems lack a unique bulk DOS, with different prescriptions representing inequivalent bulk physics. Here, we show that this apparent ambiguity is largely illusory. For any finite-range tight-binding Hamiltonian, we establish a universal bulk structure: all DOS definitions arising as thermodynamic limits of finite systems share identical multipole moments and generate identical bulk dynamics at finite times and for observables measured far from boundaries. This universality is intimately tied to the thermodynamic Green's functions, which we show to be independent of the boundary condition for large enough complex frequencies. Among all equivalent descriptions, we identify the Brown measure - obtained via Hermitization and resolvent analysis - as a canonical and convenient representative of the bulk DOS, defined directly from the infinite-volume Hamiltonian. We further show that point-gap topology imposes additional universal constraints: boundary-dependent Green's functions are forced to coincide throughout topologically trivial point gaps. This, in particular, provides a systematic criterion, valid in arbitrary dimension, for determining where and how eigenvalues of different boundary truncations can accumulate in the complex plane, and precisely delineates the regime in which the DOS ambiguity retains physical significance.
