发表机构
Donostia International Physics Center; IKERBASQUE, Basque Foundation for Science; Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel（多诺斯蒂亚国际物理中心; 伊卡巴斯基克，巴斯克科学基金会; 格勒诺布尔阿尔卑斯大学，法国国家科学研究中心，格勒诺布尔理工学院，内耳研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出利用谱局域化算符作为辅助零维哈密顿量，系统构造适用于晶体和非晶体系统的简单实空间拓扑不变量，覆盖此前难以处理的多种拓扑相。
AI 中文摘要
尽管对无相互作用拓扑物态已有详尽的理解，但目前尚无单一方法能够系统地提供简单、数值高效的拓扑不变量，并适用于所有晶体和非晶体系统。在此，我们重新审视由哈密顿量和位置算符构造的谱局域化算符，并展示如何将其视为一个辅助的零维哈密顿量，其拓扑编码了母哈密顿量的高维相。其分类将每个拓扑不变量简化为矩阵签名或相应局域化算符的Pfaffian符号，两者都易于解释且在实空间中计算高效。我们通过推导弱晶体相和旋转不变晶体相的简单实空间不变量来验证该方法，这些相此前超出了谱局域化形式主义的适用范围，还包括逃逸散射不变量的原子极限、规避基于对称性指标方法的相，以及此前没有已知不变量的相。我们的工作为晶体或非晶体系统提供了系统地构造任何无相互作用拓扑不变量的方法，为分类和预测此前未探索材料类别的拓扑开辟了途径。
英文摘要
Despite the exhaustive understanding gathered around non-interacting topological states of matter, there is no single method capable of systematically delivering simple, numerically efficient topological invariants that is applicable to all crystalline and non-crystalline systems alike. Here we revisit the spectral localizer operator, constructed from the Hamiltonian and position operators, and show how it can be treated it as an auxiliary zero-dimensional Hamiltonian whose topology encodes the higher dimensional phases of the parent Hamiltonian. Its classification reduces every topological invariant to a matrix signature or the sign of a Pfaffian for an appropriate localizer, both of which are simple to interpret and efficient to compute in real space. We validate this approach by deriving simple real-space invariants for weak and rotationally invariant crystalline phases that were previously beyond the grasp of the spectral localizer formalism, atomic limits that escape scattering invariants, phases that evade symmetry-based indicator methods, as well as phases that had no previously known invariant. Our work provides a systematic way to construct any non-interacting topological invariant for a crystalline or non-crystalline systems, opening avenues to classify and predict the topology of previously unexplored classes of materials.
Comments21 pages, 4 figures
