irbasis: Open-source database and software for intermediate-representation basis functions of imaginary-time Green’s function

Chikano, Naoya; Yoshimi, Kazuyoshi; Otsuki, Junya; Shinaoka, Hiroshi

doi:10.1016/j.cpc.2019.02.006

Cited by 46 publications

(55 citation statements)

References 17 publications

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“…where T l (x) are Chebyshev polynomials of the first kind and x(τ ) = 2τ /β − 1. In the IR basis [51] F α l (τ ) ≡ U α l (τ ) (5) where U α l (τ ) depend on the statistics and a dimensionless parameter Λ = βω max with a cutoff frequency ω max . Appendix A summarizes notations for Chebyshev and IR.…”

Section: A General Description and Notationmentioning

confidence: 99%

“…Compact representations of Green's functions are crucial to address this problem. Representations based on power meshes [44,45], Legendre polynomials [27,46], Chebyshev polynomials [47,48], intermediate numerical representations (IR) [49][50][51], quadrature rules [52,53], and spline interpolations [28] have been proposed, as well as high frequency tail expansions [54][55][56].…”

Section: Introductionmentioning

confidence: 99%

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Sparse sampling approach to efficient ab initio calculations at finite temperature

Wallerberger

Chikano

et al. 2020

Phys. Rev. B

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Efficient ab initio calculations of correlated materials at finite temperature require compact representations of the Green's functions both in imaginary time and Matsubara frequency. In this paper, we introduce a general procedure which generates sparse sampling points in time and frequency from compact orthogonal basis representations, such as Chebyshev polynomials and intermediate representation (IR) basis functions. These sampling points accurately resolve the information contained in the Green's function, and efficient transforms between different representations are formulated with minimal loss of information. As a demonstration, we apply the sparse sampling scheme to diagrammatic GW and GF2 calculations of a hydrogen chain, of noble gas atoms and of a silicon crystal.arXiv:1908.07575v1 [cond-mat.str-el]

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Section: A General Description and Notationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sparse sampling approach to efficient ab initio calculations at finite temperature

Wallerberger

Chikano

et al. 2020

Phys. Rev. B

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“…Alternatives such as uniform power meshes have had some success 45,46 . However, the most compact representations are achieved using a set of (orthogonal) continuous basis functions directly in imaginary time, such as orthogonal polynomials 47,48 or numerical basis functions [49][50][51][52][53] . The convergence of such a representation is faster than exponential, 47,48 and asymptotically superior to any polynomially converging representation.…”

Section: Introductionmentioning

confidence: 99%

Legendre-spectral Dyson equation solver with super-exponential convergence

Dong

Zgid

Gull

et al. 2020

The Journal of Chemical Physics

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Quantum many-body systems in thermal equilibrium can be described by the imaginary time Green's function formalism. However, the treatment of large molecular or solid ab inito problems with a fully realistic Hamiltonian in large basis sets is hampered by the storage of the Green's function and the precision of the solution of the Dyson equation. We present a Legendre-spectral algorithm for solving the Dyson equation that addresses both of these issues. By formulating the algorithm in Legendre coefficient space, our method inherits the known faster-than-exponential convergence of the Green's function's Legendre series expansion. In this basis, the fast recursive method for Legendre polynomial convolution, enables us to develop a Dyson equation solver with quadratic scaling. We present benchmarks of the algorithm by computing the dissociation energy of the helium dimer He 2 within dressed second-order perturbation theory. For this system, the application of the Legendre spectral algorithm allows us to achieve an energy accuracy of 10 −9 E h with only a few hundred expansion coefficients. arXiv:2001.11603v2 [cond-mat.str-el] 5 Apr 2020

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“…A library is provided with precomputed numerical data of the basis functions. 110,111) It allows us to use the IR basis as easily as classical orthogonal polynomials.…”

Section: Mathematical Properties Of Ir Basis Functionsmentioning

confidence: 99%

Sparse Modeling in Quantum Many-Body Problems

et al. 2020

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This review paper describes the basic concept and technical details of sparse modeling and its applications to quantum many-body problems. Sparse modeling refers to methodologies for finding a small number of relevant parameters that well explain a given dataset. This concept reminds us physics, where the goal is to find a small number of physical laws that are hidden behind complicated phenomena. Sparse modeling extends the target of physics from natural phenomena to data, and may be interpreted as "physics for data". The first half of this review introduces sparse modeling for physicists. It is assumed that readers have physics background but no expertise in data science. The second half reviews applications. Matsubara Green's function, which plays a central role in descriptions of correlated systems, has been found to be sparse, meaning that it contains little information. This leads to (i) a new method for solving the illconditioned inverse problem for analytical continuation, and (ii) a highly compact representation of Matsubara Green's function, which enables efficient calculations for quantum many-body systems. 1 arXiv:1911.04116v1 [cond-mat.str-el]

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irbasis: Open-source database and software for intermediate-representation basis functions of imaginary-time Green’s function

Cited by 46 publications

References 17 publications

Sparse sampling approach to efficient ab initio calculations at finite temperature

Sparse sampling approach to efficient ab initio calculations at finite temperature

Legendre-spectral Dyson equation solver with super-exponential convergence

Sparse Modeling in Quantum Many-Body Problems

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