第一性原理BSE方法计算固体材料激子能谱的准确度评估

激子是固体材料最重要的元激发之一，在光与物质的相互作用和玻色凝聚等方面扮演重要角色。激子是一种典型的多体相互作用。描述激子性质的最重要的两个定量指标是激子能量和结合能。第一性原理方法求解Bethe-Salpeter方程(BSE)是当下研究固体材料，尤其是低维系统激子性质的重要工具。现代第一性原理计算常存在系统性偏差，典型案例是密度泛函理论对能隙的系统低估。但第一性原理BSE方法计算激子能量和结合能等是否存在系统性偏差尚不清楚也未见研究。本项目旨在通过对典型固体材料第一性原理BSE计算结果的数理统计分析，评估该方法计算激子能谱的精度并数据定标。于定性和定量层面上建立DFT能带结构，GW自能修正和Tamm-Dancoff近似对激子能量和结合能等性质的影响规律，揭示物理成因及可能的误差抵消效应，形成对进一步优化使用第一性原理BSE方法研究固体材料激发态性质的改进建议。

Exciton is one of the most important elementary excitations in solids and plays an important role in the interaction between light and matter, as well as Bose condensation. Exciton represents a typical many-body interaction. Exciton energy and binding energy are the two single-most important physical parameters to describe the excitonic properties. At present, first-principles Bethe-Salpeter equation (BSE) calculation is an important tool for studying the excitons in solids, especially in low-dimensional systems. Modern first-principles calculations usually have a systematic error. A typical case is the underestimation of energy gap by density functional theory. However, it is not clear whether the first-principles BSE method has systematic error in calculating exciton energy and binding energy. The purpose of this project is to evaluate the accuracy of the method for calculating excitonic properties and to calibrate the data through mathematical statistical analysis of the results for typical solids. The effects of GW self-consistency, exchange-correlation functionals and Tamm-Dancoff approximation on excitonic properties will be unraveled both qualitatively and quantitatively, as well as the underlying physics. Suggestions would be made to further improve the accuracy in calculating the excitonic properties of solids using first-principles BSE method.