The fundamental gap of an interacting many-electron system is given by the sum of the single-particle Kohn-Sham gap and the derivative discontinuity. The latter can be generated by advanced approximations to the exchange-correlation (XC) energy and is the key quantity to capture strong correlation with density functional theory (DFT). In this work we derive an expression for the derivative discontinuity in terms of the XC kernel of time-dependent density functional theory and demonstrate the crucial role of a discontinuity in the XC kernel itself. By relating approximate XC kernels to approximate local vertex corrections we then generate beyond-GW self-energies that include a discontinuity in the local vertex function. The quantitative importance of this result is illustrated with a numerical study of the local exchange vertex on model systems.
我们提出并实现了镶木地板近似的双费米子形式主义的基础上的部分玻色子化的对偶顶点函数，大大降低了计算的计算成本。该方法依赖于将顶点精确地分裂成单玻色子交换贡献和剩余的四个费米子顶点，它们在物理上分别体现了长程和短程空间相关性。在根据剩余顶点重铸镶木地板方程之后，使用Eckhardt等人的截断单位法[Phys. Rev. B 101，155104（2020）]求解这些方程，该方法允许在不同状态下快速收敛形状因子的数量。虽然我们对镶木地板方程的数值处理可以仅限于几个松原频率，这让人想起Astretsov等人[Phys. Rev. B 101，075109（2020）]，但单粒子和双粒子光谱信息被完全保留。在二维哈伯德模型的应用中，该方法同意在很宽的参数范围内的图的随机求和定量。
Tensor hypercontraction for self-consistent vertex corrected GW with static and dynamic screening; applications to molecules and solids with superexchange
Vertex corrections in the dynamic structure factor in spin ladders
我们将微扰连续么正变换的结果与平均场计算相结合，以确定单模的演化，即，一个三重子，在温度从零升高到有限值时对两腿$S=1/2$梯的动态结构因子的贡献。温度依赖性由两个效应引起：（i）在存在热激活的三体子的横档上不能激发三体子;（ii）如果存在热激活的三体子，则发生条件激发过程。这两种效应都会在加热时减少一个三重子的光谱权重。结果表明，第二种效应是在计算动态结构因子时的主导顶点修正。本文用微扰方法计算了具有附加四自旋环交换的两腿海森堡阶梯中条件三重子激发的矩阵元，最高可达9阶。计算结果进行了比较的非弹性中子散射实验上的铜梯形化合物La $_{4}$ Sr $_{10}$ Cu $_{24}$ O $_{41}$显示令人信服的协议为已建立的值的交换常数。
