Sparse sampling and tensor network representation of two-particle Green's functions

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Authors	SHINAOKA Hiroshi GEFFROY Dominique Alain WALLERBERGER Markus OTSUKI Junya YOSHIMI Kazuyoshi GULL Emanuel KUNES Jan
Year of publication	2020
Type	Article in Periodical
Magazine / Source	SciPost Physics
MU Faculty or unit	Faculty of Science
Citation
Web	https://scipost.org/10.21468/SciPostPhys.8.1.012
Doi	http://dx.doi.org/10.21468/SciPostPhys.8.1.012
Keywords	Green's function; Hubbard model; Tensor networks
Description	Many-body calculations at the two-particle level require a compact representation of two-particle Green's functions. In this paper, we introduce a sparse sampling scheme in the Matsubara frequency domain as well as a tensor network representation for two-particle Green's functions. The sparse sampling is based on the intermediate representation basis and allows an accurate extraction of the generalized susceptibility from a reduced set of Matsubara frequencies. The tensor network representation provides a system independent way to compress the information carried by two-particle Green's functions. We demonstrate efficiency of the present scheme for calculations of static and dynamic susceptibilities in single- and two-band Hubbard models in the framework of dynamical mean-field theory.
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