sparse-ir: Optimal compression and sparse sampling of many-body propagators

Wallerberger, Markus; Badr, Samuel; Hoshino, Shintaro; Kakizawa, Fumiya; Koretsune, Takashi; Nagai, Yuki; Nogaki, Kosuke; Nomoto, Takuya; Mori, Hitoshi; Otsuki, Junya; Ozaki, Soshun; Sakurai, Rihito; Vogel, Constanze; Niklas, Witt,; Yoshimi, Kazuyoshi; Shinaoka, Hiroshi

doi:10.1016/j.softx.2022.101266

Cited by 24 publications

(13 citation statements)

References 42 publications

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“…Dynamic quantities, including fermionic and bosonic functions, are expanded into the intermediate representation (IR) with sparse sampling on both the imaginary-time and Matsubara frequency axes . Both the IR basis and the sampling points are generated using sparse-ir open-source software package.…”

Section: Computational Detailsmentioning

confidence: 99%

Low-Scaling Algorithm for the Random Phase Approximation Using Tensor Hypercontraction with k-point Sampling

Yeh,

Morales

2023

J. Chem. Theory Comput.

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We present a low-scaling algorithm for the random phase approximation (RPA) with k-point sampling in the framework of tensor hypercontraction (THC) for electron repulsion integrals (ERIs). The THC factorization is obtained via a revised interpolative separable density fitting (ISDF) procedure with a momentumdependent auxiliary basis for generic single-particle Bloch orbitals. Our formulation does not require preoptimized interpolating points or auxiliary bases, and the accuracy is systematically controlled by the number of interpolating points. The resulting RPA algorithm scales linearly with the number of k-points and cubically with the system size without any assumption on sparsity or locality of orbitals. The errors of ERIs and RPA energy show rapid convergence with respect to the size of the THC auxiliary basis, suggesting a promising and robust direction to construct efficient algorithms of higher order many-body perturbation theories for large-scale systems.

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Section: Computational Detailsmentioning

confidence: 99%

Low-Scaling Algorithm for the Random Phase Approximation Using Tensor Hypercontraction with k-point Sampling

Yeh,

Morales

2023

J. Chem. Theory Comput.

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“…Dynamic quantities, including both Fermionic and bosonic functions, are expanded into the intermediate representation (IR) with sparse sampling on both the imaginary-time and Matsubara frequency axes . Both the IR basis and the sampling points are generated using the open-source software package.…”

Section: Computational Detailsmentioning

confidence: 99%

Low-Scaling Algorithms for GW and Constrained Random Phase Approximation Using Symmetry-Adapted Interpolative Separable Density Fitting

Yeh,

Morales

2024

J. Chem. Theory Comput.

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We present low-scaling algorithms for GW and constrained random phase approximation based on a symmetryadapted interpolative separable density fitting (ISDF) procedure that incorporates the space-group symmetries of crystalline systems. The resulting formulations scale cubically, with respect to system size, and linearly with the number of k-points, regardless of the choice of single-particle basis and whether a quasiparticle approximation is employed. We validate these methods through comparisons with published literature and demonstrate their efficiency in treating large-scale systems through the construction of downfolded many-body Hamiltonians for carbon dimer defects embedded in hexagonal boron nitride supercells. Our work highlights the efficiency and general applicability of ISDF in the context of large-scale many-body calculations with k-point sampling beyond density functional theory.

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“…They therefore yield exceptionally compact representations with controllable, high-order accuracy. Fortran, Python, and Julia libraries are available for both the IR with sparse sampling [15] and the DLR [16]. Low rank Green's function representations have been used to solve self-consistent diagrammatic equations in a variety of applications, including the SYK model [14,16,17], the self-consistent finite temperature GW method [13,18], Eliashberg-type equations for superconductivity [19][20][21][22], and Bethe-Salpeter-type equations for Hubbard models [23].…”

Section: Introductionmentioning

confidence: 99%

Low rank Green's function representations applied to dynamical mean-field theory

Sheng¹,

Hampel²,

Beck³

et al. 2023

Preprint

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Several recent works have introduced highly compact representations of single-particle Green's functions in the imaginary time and Matsubara frequency domains, as well as efficient interpolation grids used to recover the representations. In particular, the intermediate representation with sparse sampling and the discrete Lehmann representation (DLR) make use of low rank compression techniques to obtain optimal approximations with controllable accuracy. We consider the use of the DLR in dynamical mean-field theory (DMFT) calculations, and in particular show that the standard full Matsubara frequency grid can be replaced by the compact grid of DLR Matsubara frequency nodes. We test the performance of the method for a DMFT calculation of Sr2RuO4 at temperature 50 K using a continuous-time quantum Monte Carlo impurity solver, and demonstrate that Matsubara frequency quantities can be represented on a grid of only 36 nodes with no reduction in accuracy, or increase in the number of self-consistent iterations, despite the presence of significant Monte Carlo noise.

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sparse-ir: Optimal compression and sparse sampling of many-body propagators

Cited by 24 publications

References 42 publications

Low-Scaling Algorithm for the Random Phase Approximation Using Tensor Hypercontraction with k-point Sampling

Low-Scaling Algorithm for the Random Phase Approximation Using Tensor Hypercontraction with k-point Sampling

Low-Scaling Algorithms for GW and Constrained Random Phase Approximation Using Symmetry-Adapted Interpolative Separable Density Fitting

Low rank Green's function representations applied to dynamical mean-field theory

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