模型研究与计算  

Model study and numerical calculation

作　　者：牛谦 乔振华 任亚飞 NIU Qian;QIAO Zhen-Hua;REN Ya-Fei(School of Physical Sciences,University of Science and Technology of China,Hefei 230026,China;Department of Physics and Astronomy,University of Delaware,Newark DE19716,USA)

机构地区：[1]中国科学技术大学物理学院,合肥230026 [2]美国特拉华大学物理与天文系,纽瓦克DE19716

出　　处：《物理》2025年第2期83-94,共12页Physics

基　　金：国家自然科学基金(批准号:12234017,12474158,12488101)资助项目。

摘　　要：文章系统综述拓扑物态及量子几何效应研究中的关键理论模型与计算方法。Hofstadter蝴蝶模型揭示了强磁场下电子能谱的分形结构及其与贝里曲率的联系;基于六角晶格的系列理论(石墨烯、Haldane与Kane-Mele模型)预言了量子反常霍尔效应及受丰富的对称性保护的拓扑绝缘态;低能连续模型帮助人们解析地理解拓扑相变与边界态;第一性原理计算结合瓦尼尔插值实现了材料中贝里曲率的定量计算与反常输运性质预测;无序系统模型研究则阐明了拓扑态的鲁棒性、无序诱导的拓扑相变规律及陈数湮灭机制。文章强调模型与计算方法在量子几何理论、拓扑材料设计中的基础地位。This paper introduces representative theoretical models and calculation methods that are central to the study of topological phases and quantum geometric effects.Specifically,the Hofstadter butterfly model unravels the fractal electronic spectrum and its intrinsic connection with geometric phases under strong magnetic fields.Honeycomb latticebased models,including graphene,Haldane,and Kane-Mele models,have demonstrated the existence of quantum anomalous Hall effects and symmetry-protected topological phases.Low-energy continuum models provide a valuable analytical understanding of topological phases,phase transitions,and edge-mode formation.First-principles calculations combined with Wannier function interpolation enable quantitative calculation of Berry curvatures and anomalous transport in real materials.Disorder models elucidate the robustness of topological phases,disorder-induced topological phase transitions,and Chern number annihilation mechanisms.We emphasize the fundamental importance of theoretical models and computational methods in developing the theory of quantum geometry and topological materials.

关 键 词：六角晶格 连续模型 第一原理计算 量子几何 贝里曲率 拓扑态 无序 局域化 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]