A modified $GW$ approximation to many-body systems is developed. The approximation has the same computational complexity as the traditional $GW$ approach, but uses a different truncation scheme. This scheme neglects the high-order connected correlation functions. A covariant (preserving the Ward identities due to the charge conservation) scheme for the two-body correlators is employed, which holds the relation between the charge correlator and the charge susceptibility. The method is tested on the two-dimensional one-band Hubbard model. The results are compared with exact diagonalization, the $GW$ approximation, the fluctuation-exchange (FLEX) theory, and determinantal Monte Carlo approach. The comparison for the (one-body) Green's function demonstrates that it is more precise in the strong-coupling regime (especially away from half filling) than the $GW$ and FLEX approximations, which have a similar complexity. More importantly, this method indicates a Mott-Hubbard gap as the Hubbard $U$ increases, whereas the $GW$ and FLEX methods fail. In addition, the charge correlator obtained from the covariant scheme not only holds the consistency of the static charge susceptibility, but also makes a significant improvement over the random phase approximation calculations.

中文翻译：

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电子系统中的改良GW方法

一个修改 $G宽$开发了多体系统的近似。近似具有与传统的相同的计算复杂度$G宽$方法，但使用不同的截断方案。该方案忽略了高阶连通相关函数。对二体相关器采用协变（由于电荷守恒而保留 Ward 恒等式）方案，该方案保持电荷相关器与电荷磁化率之间的关系。该方法在二维一波段哈伯德模型上进行了测试。结果与精确对角化进行比较，$G宽$近似、波动交换 (FLEX) 理论和行列式蒙特卡罗方法。（一体）格林函数的比较表明，它在强耦合状态下（尤其是远离半填充）比在强耦合状态下更精确。$G宽$和 FLEX 近似，它们具有相似的复杂性。更重要的是，这种方法表明 Mott-Hubbard 间隙为 Hubbard$你$ 增加，而 $G宽$和 FLEX 方法失败。此外，从协变方案得到的电荷相关器不仅保持了静电荷磁化率的一致性，而且对随机相位近似计算也有显着改进。