First-principles calculation method for periodic system under external electromagnetic field

Abstract

The exploration of electromagnetic field influences on material characteristics remains a pivotal concern within scientific investigations. Nonetheless, in the realm of computational condensed matter physics, traditional density functional theory's extrapolation to scenarios inclusive of external electromagentic fields poses considerable challenges. These issues largely stem from the disruption of translational symmetry by external fields inherent in periodic systems, rendering Bloch's theorem inoperative. Consequently, the employment of first-principles methodologies in calculating material properties in the presence of external fields becomes an intricate task, especially in circumstances where the external field cannot be approximated as a minor perturbation. Over the past two decades, a significant number of scholars within the field of computational condensed matter physics have dedicated their work towards the formulation and refinement of first-principles computational methodologies adept at handling periodic systems subjected to finite external fields. This paper endeavors to systematically recapitulate these theoretical methodologies and their application across a broad spectrum including, but not limited to, ferroelectric, piezoelectric, ferromagnetic, and multiferroic domains. In the initial segment of this paper, we provide a succinct exposition on modern theory of polarization and delineate the process of constructing two methodologies for computations in finite electric fields predicated on this theory in conjunction with density functional theory. The succeeding segment delves into the integration of external magnetic fields into density functional theory and examines the accompanying computational procedures alongside the challenges they present. In the third segment, we firstly reflect on the first-principles effective Hamiltonian method, prevalent in the study of magnetic, ferroelectric and multiferroic systems, along with its adaptations for situations involving external fields. Concluding the paper, we introduce the exciting developments in constructing effective Hamiltonian models using neural network methods from machine learning, and their extensions under consideration of external fields.

Modeling ferroelectric phase transitions with graph convolutional neural networks

“…相对位移 [58] . 对于这一过程, 在早期曾尝试通过以 公式为核心的方法进行建模 [64] , 但是单硫族化合 物中存在特殊的"超键 (metavalent bond)" [65] , 并 没有清晰的软模概念, 因此在利用有效哈密顿量方 法对其势能面建模时存在较大困难 [66] , 而图卷积 神经网络避免了人为构建能量函数, 通过消息传递 过程自动学习原子之间的相互作用, 从而更加方 便、高效地对单硫族化合物的势能面进行建模. 从 这个意义上说, 图卷积神经网络可以视为"无需物 理先验知识的有效哈密顿量方法" [67] .…”

“…具体而言, 这类材料与典型钙钛矿铁电体(例如 BaTiO 3 )不同, 其中原子间具有很强的非线性相互 作用, 并且这一非线性相互作用不能通过偶极-偶 极间相互作用分离出来, 所以难以提取出软模并用 有效哈密顿量方法处理 [64,66] . 因此, 目前对于单硫 族化合物的势能面建模缺少一个统一、优美的方 法.…”