论文标题
G1 - G2方案：Hartree-fock-GKBA中非平衡绿色功能模拟的急剧加速
The G1--G2 Scheme: Dramatic Acceleration of Nonequilibrium Green Functions Simulations Within the Hartree--Fock-GKBA
论文作者
论文摘要
外部激发后量子多体系统的时间演变引起了许多领域的浓厚兴趣。这些过程的理论建模是具有挑战性的，并且可以在两个和三个维度上处理相关费物的唯一严格的量子动力学方法是非平衡绿色功能（NEGF）。但是，由于模拟持续时间$ t $，NEGF模拟在计算上昂贵。最近，对于二阶Born（SOA）自我化的广义Kadanoff--Baym Ansatz（GKBA），实现了$ t^2 $ - 尺度，该自我造型已大大扩展了NEGF模拟的范围。在最近的字母[schlünzen\ textit {et al。}，物理。莱特牧师。 \ textbf {124}，076601（2020）]我们证明了GKBA-NEGF模拟可以有效地映射到单个粒子和两粒子绿色功能上的耦合的时间局部方程上，因此该方法称为G1-g2方案。这允许一个人使用$ t^1 $尺度的订单进行相同的模拟，无论是SOA还是$ GW $自我的自我素，从而引起了巨大的加速。在这里，我们介绍了有关G1-G2方案的更多详细信息，包括基本方程的推导，包括一般结果，Hubbard系统和Jellium。另外，我们演示了如何将初始相关性纳入G1-G2方案。此外，派生延伸到更广泛的自身能力类别，包括粒子和粒子 - 孔通道中的$ t $矩阵以及动态筛选的磁通近似。最后，我们证明，与我们的第一份报告相比，G1-G2方案的CPU时间缩放可以改善G1-G2方案的CPU时间缩放，与我们的第一份报告相比：与原始GKBA相比，间接费用不超过另一个因素$ n_b $。
The time evolution in quantum many-body systems after external excitations is attracting high interest in many fields. The theoretical modeling of these processes is challenging, and the only rigorous quantum-dynamics approach that can treat correlated fermions in two and three dimensions is nonequilibrium Green functions (NEGF). However, NEGF simulations are computationally expensive due to their $T^3$-scaling with the simulation duration $T$. Recently, $T^2$-scaling was achieved with the generalized Kadanoff--Baym ansatz (GKBA), for the second-order Born (SOA) selfenergy, which has substantially extended the scope of NEGF simulations. In a recent Letter [Schlünzen \textit{et al.}, Phys. Rev. Lett. \textbf{124}, 076601 (2020)] we demonstrated that GKBA-NEGF simulations can be efficiently mapped onto coupled time-local equations for the single-particle and two-particle Green functions on the time diagonal, hence the method has been called G1--G2 scheme. This allows one to perform the same simulations with order $T^1$-scaling, both for SOA and $GW$ selfenergies giving rise to a dramatic speedup. Here we present more details on the G1--G2 scheme, including derivations of the basic equations including results for a general basis, for Hubbard systems and for jellium. Also, we demonstrate how to incorporate initial correlations into the G1--G2 scheme. Further, the derivations are extended to a broader class of selfenergies, including the $T$ matrix in the particle--particle and particle--hole channels, and the dynamically screened-ladder approximation. Finally, we demonstrate that, for all selfenergies, the CPU time scaling of the G1--G2 scheme with the basis dimension, $N_b$, can be improved compared to our first report: the overhead compared to the original GKBA, is not more than an additional factor $N_b$.
