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arXiv · 1803.01916

Overcomplete compact representation of two-particle Green's functions

Hiroshi Shinaoka·Junya Otsuki·Kristjan Haule·Markus Wallerberger·Emanuel Gull·Kazuyoshi Yoshimi·Masayuki Ohzeki
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Abstract

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.

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Hiroshi Shinaoka, Junya Otsuki, Kristjan Haule, Markus Wallerberger, Emanuel Gull, Kazuyoshi Yoshimi, Masayuki Ohzeki. 2018-05-10. Overcomplete compact representation of two-particle Green's functions. https://doi.org/10.1103/physrevb.97.205111

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