Overcomplete compact representation of two-particle Green's functions

Two-particle Green's functions and the vertex functions play a critical role in theoretical frameworks for describing strongly correlated electron systems. However, numerical calculations at two-particle level often suffer from large computation time and massive memory consumption. We derive a general expansion formula for the two-particle Green's functions in terms of an overcomplete representation based on the recently proposed "intermediate representation" basis. The expansion formula is obtained by decomposing the spectral representation of the two-particle Green's function. We demonstrate that the expansion coefficients decay exponentially, while all high-frequency and long-tail structures in the Matsubara-frequency domain are retained. This representation therefore enables efficient treatment of two-particle quantities and opens a route to the application of modern many-body theories to realistic strongly correlated electron systems.

两粒子格林函数和顶角函数在描述强关联电子系统的理论框架中起着关键作用。然而，两粒子层面的数值计算往往面临计算时间长和内存消耗大的问题。我们基于最近提出的“中间表象”基，依据一种超完备表象推导出了两粒子格林函数的一个通用展开公式。该展开公式是通过分解两粒子格林函数的谱表示得到的。我们证明了展开系数呈指数衰减，同时在松原频率域中所有高频和长尾结构都得以保留。因此，这种表象能够有效地处理两粒子量，并为将现代多体理论应用于实际的强关联电子系统开辟了一条途径。