论文标题
在为非铁质系统和对角度问题的问题上选择物理有意义的拓扑分类时
On Choosing a Physically Meaningful Topological Classification for Non-Hermitian Systems and the Issue of Diagonalizability
论文作者
论文摘要
Hermitian操作员的拓扑分类仅取决于某些离散对称性的存在或不存在。对于非热门操作员，我们还需要指定光谱间隙的类型。它们具有点间隙或线间隙的风味。由于线间隙的存在意味着存在点差距，因此通常有多个适用于物理系统的数学分类。这提出了一个问题：这些差距型分类中的哪一个具有物理意义？ 为了决定这个问题，我提出了一个简单的标准，即对身体相关状态的选择。这概括了费米投影的概念，该概念在费米金冷凝物质系统的拓扑分类中起着至关重要的作用，并作为光子和宏伟晶体的整体分类中的辅助数量进入。之后，分类完全是算法，系统的拓扑是用对称和约束的（对）投影（对）的。我的调查中的一个关键点是对角度的相关性。即使对于非热系统的现有拓扑分类，也必须假定对角度差异，以确保哈密顿量的持续变形导致光谱，预测和一级人员的持续变形。
The topological classification of hermitian operators is solely determined by the presence or absence of certain discrete symmetries. For non-hermitian operators we in addition need to specify the type of spectral gap. They come in the flavor of a point gap or a line gap. Since the presence of a line gap implies the existence of a point gap, there is usually more than one mathematical classification applicable to a physical system. That raises the question: which of these gap-type classifications is physically meaningful? To decide this question, I propose a simple criterion, namely the choice of physically relevant states. This generalizes the notion of Fermi projection that plays a crucial role in the topological classification of fermionic condensed matter systems, and enters as an auxiliary quantity in the bulk classification of photonic and magnonic crystals. After that the classification is entirely algorithmic, the system's topology is encoded in (pairs of) projections with symmetries and constraints. A crucial point in my investigation is the relevance of diagonalizability. Even for existing topological classifications of non-hermitian systems diagonalizability needs to be assumed to ensure that continuous deformations of the hamiltonian lead to continuous deformations of the spectra, projections and unitaries.
