Overcomplete compact representation of two-particle Green's functions

Shinaoka, Hiroshi; Otsuki, Junya; Haule, Kristjan; Wallerberger, Markus; Gull, Emanuel; Yoshimi, Kazuyoshi; Ohzeki, Masayuki

doi:10.1103/physrevb.97.205111

Cited by 36 publications

(26 citation statements)

References 55 publications

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“…Two-particle quantities are difficult to handle even in effective model calculations due to the multiple indices for frequencies and spin/orbital degrees of freedom. The IR basis has recently been extended to two-particle quantities [66]. The application of the sparse sampling scheme to two-particle quantities is an interesting topic for future research.…”

Section: Discussionmentioning

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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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: Discussionmentioning

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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“…This is achieved by projecting the self-energy onto a physical compact basis and filtering out noise due to the discretization of a continuous bath. The present method is based on the recently shown fact that the imaginarytime/Matsubara Green's functions are sparse at finite T : the imaginary-time/frequency dependence of these Green's functions can be represented by a few dozen basis functions of the so-called intermediate representation (IR) basis [10][11][12][13]. In the previous study [10], they used this representation together with sparse modeling (SpM) techniques in data science to extract noise-insensitive spectral functions from QMC data [10].…”

Section: Introductionmentioning

confidence: 99%

Smooth Self-energy in the Exact-diagonalization-based Dynamical Mean-field Theory: Intermediate-representation Filtering Approach

Nagai

Shinaoka

2019

J. Phys. Soc. Jpn.

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We propose a method for estimating smooth real-frequency self-energy in the dynamical meanfield theory with the finite-temperature exact diagonalization (DMFT-ED). One of the benefits of DMFT-ED calculations is that one can obtain real-frequency spectra without a numerical analytic continuation. However, these spectra are spiky and strongly depend on the way to discretize a continuous bath (e.g., the number of the bath sites). The present scheme is based on a recently proposed compact representation of imaginary-time Green's functions, the intermediate representation (IR). The projection onto the IR basis acts as a noise filter for the discretization errors in the self-energy. This enables to extract the physically relevant part from the noisy self-energy. We demonstrate the method for single-site DMFT calculations of the single-band Hubbard model. We also show the results can be further improved by numerical analytic continuation.

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“…As in the literature [1], the method can efficiently find reasonably the density of states without any prior knowledge. In addition, the proposed method elucidate the sparse representation for the QMC data [2,18]. The sparse representation is useful for compression of the QMC data and finding the physical relevant feature from it.…”

Section: Discussionmentioning

confidence: 99%

Sparse modeling for Quantum Monte-Carlo simulation

Ohzeki¹

2018

J. Phys.: Conf. Ser.

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Abstract. We show a new kind of applications of the sparse modeling to a traditional problem in the condensed-matter physics. In the quantum Monte-Carlo simulation, we observe a huge amount of data for investigation of the details of the low-energy behavior for interacting manybody systems. Although the real-time behavior is actually under investigation, the quantum Monte-Carlo simulation is performed on the imaginary time for restriction of the method. Thus we need a technique for analytical continuation connecting between the real and imaginarytime functions. However the analytical continuation can be problematic because the problem consists of solving the ill-conditioned equation. In the present study, by employing an adequate regularization, we solve efficiently the ill-conditioned equation in the analytical continuation. As a result, we have a novel way to perform the analytical continuation and find an intermediate representation between imaginary-time and real-frequency domains. IntroductionIn the present manuscript, we provide an elementary guide for our recent papers from manybody physics to fascinating applications of the sparse modeling [1,2]. In the analysis on the condensed matter, it is harmful to directly deal with the theoretical model for investigating some nontrivial aspects. We usually employ various approximate method and numerical calculations. In the quantum many-body systems, most of the analyses are performed with recourse to the imaginary-time framework for computing the real-time behavior. Then one needs to utilize the analytical continuation to transform the estimated quantities in imaginary-time regions to real-frequency regions, which can be compared to the experimental results. The representative method to deal with the quantum many-body systems is the elaborate diagrammatic approach widely used for investigating both of static and dynamics responses of the systems [3,4]. Variants of the quantum Monte-Carlo simulations (QMC) also take full advantage of imaginary-time descriptions [5,6]. We consider the case of the QMC in the following.The analytical continuation can be formulated as the inverse problem. Given the relationship between imaginary-time description G and the real-frequency behavior ρ as

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Overcomplete compact representation of two-particle Green's functions

Cited by 36 publications

References 55 publications

Sparse sampling approach to efficient ab initio calculations at finite temperature

Sparse sampling approach to efficient ab initio calculations at finite temperature

Smooth Self-energy in the Exact-diagonalization-based Dynamical Mean-field Theory: Intermediate-representation Filtering Approach

Sparse modeling for Quantum Monte-Carlo simulation

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