Abstract
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.
Highlights
For fixed values of ωmax and β, the intermediate representation (IR) basis functions are defined through the singular value decomposition (SVD)
The local 2P Green’s function Gloc is sampled on a non-uniform grid in the Matsubara frequency domain, shown in Fig. 2 (Λ = 104, Nl = 24), using a modified version of the ALPS/CT-HYB impurity solver [35, 36] based on the continuous-time hybridization expansion algorithm [37, 38]
Based on the IR basis, we have introduced a procedure for generating sparse grids in the Matsubara frequency domain and a fitting algorithm based on a tensor network representation
Summary
Two-particle (2P) Green’s functions are building blocks of a variety of many-body theories [1]. The frequency dependence is treated exactly in a small low-frequency box while in the outside region an asymptotic form is used This works efficiently at relatively high temperatures. We introduce a sparse grid in the Matsubara frequency domain, which contains the desired information about the 2P Green’s functions This extends the approach developed in Ref. We test the accuracy of sparse sampling and tensor network representation by calculating the static susceptibility of the single-band Hubbard model on a square lattice. We show the efficiency of the present method for dynamical susceptibility calculation for a two-band Hubbard model with low symmetry.
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