npj:神经元扮演矩阵元:从能带结构得到紧束缚哈密顿量
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来自武汉大学物理科学与技术学院的常胜教授团队,通过引入机器学习工具,提出了一种构造紧束缚哈密顿量的神经网络, 该网络模型将神经元作为紧束缚哈密顿量的矩阵元素,将给定的从头算能带结构作为训练集,可以直接学习得到紧束缚哈密顿量的在位能与跳跃能。这种动态的、一对一的神经网络能根据预定义的精度,要求自动调整网络中的神经元数量,不需要有对系统基组的先验知识,也不用输入系统的实空间信息,只需要输入想要还原的能带数据作为训练集即可。在InSe纳米带材料上通过与最局域瓦尼尔函数法得到的结果作对比,验证了该机器学习方法构造的紧束缚哈密顿量在计算系统电子和输运特性上的精度和效率。此外,该研究还给出了两种基于所提出的基本网络模型的变体模型,能分别用以优化给定的紧束缚模型,以及生成Slater-Koster形式的紧束缚模型。该研究不仅提出了一种新的构造紧束缚模型的方法,还为机器学习工具运用在物理问题中提供了新的见解。
该文近期发表于npj Computational Materials 7: 11 (2021),英文标题与摘要如下,点击左下角“阅读原文”可以自由获取论文PDF。
Machine learning method for tight-binding Hamiltonian parameterization from ab-initio band structure
Zifeng Wang, Shizhuo Ye, Hao Wang, Jin He, Qijun Huang & Sheng Chang
The tight-binding (TB) method is an ideal candidate for determining electronic and transport properties for a large-scale system. It describes the system as real-space Hamiltonian matrices expressed on a manageable number of parameters, leading to substantially lower computational costs than the ab-initio methods. Since the whole system is defined by the parameterization scheme, the choice of the TB parameters decides the reliability of the TB calculations. The typical empirical TB method uses the TB parameters directly from the existing parameter sets, which hardly reproduces the desired electronic structures quantitatively without specific optimizations. It is thus not suitable for quantitative studies like the transport property calculations. The ab-initio TB method derives the TB parameters from the ab-initio results through the transformation of basis functions, which achieves much higher numerical accuracy. However, it assumes prior knowledge of the basis and may encompass truncation error. Here, a machine learning method for TB Hamiltonian parameterization is proposed, within which a neural network (NN) is introduced with its neurons acting as the TB matrix elements. This method can construct the empirical TB model that reproduces the given ab-initio energy bands with predefined accuracy, which provides a fast and convenient way for TB model construction and gives insights into machine learning applications in physical problems.
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