Efficient 
<i>ab initio</i>
 Migdal-Eliashberg calculation considering the retardation effect in phonon-mediated superconductors

Wang, Tianchun; Nomoto, Takuya; Nomura, Yusuke; Shinaoka, Hiroshi; Otsuki, Junya; Koretsune, Takashi; Arita, Ryotaro

doi:10.1103/physrevb.102.134503

Cited by 31 publications

(24 citation statements)

References 40 publications

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“…were developed to further improve numerical efficiency. [162][163][164] The method provides momentum-and frequency-dependent self-energies in the regime of weak to intermediate coupling strength and was successfully applied to multi-band high-Tc superconductors. [104,153,154] As for future work it might be interesting to extend multiorbital TPSC to study further neighbor interactions as was already done for the single-orbital TPSC [146][147][148] or superconductivity as was already started in ref.…”

Section: Discussionmentioning

confidence: 99%

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Two‐Particle Self‐Consistent Method for the Multi‐Orbital Hubbard Model

2021

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One of the most challenging problems in solid state systems is the microscopic analysis of electronic correlations. A paramount minimal model that encodes correlation effects is the Hubbard Hamiltonian, which—regardless of its simplicity—is exactly solvable only in a few limiting cases and approximate many‐body methods are required for its solution. In this review, an overview on the non‐perturbative two‐particle self‐consistent method (TPSC), which was originally introduced to describe the electronic properties of the single‐band Hubbard model, is presented. A detailed derivation of the multi‐orbital generalization of TPSC is introduced here and particular features of the method on exemplary interacting models in comparison to dynamical mean‐field theory results are discussed.

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Section: Discussionmentioning

confidence: 99%

“…In addition, new numerical techniques were developed to further improve numerical efficiency. [ 162–164 ] The method provides momentum‐ and frequency‐dependent self‐energies in the regime of weak to intermediate coupling strength and was successfully applied to multi‐band high‐Tc superconductors. [ 104,153,154 ]…”

Section: Discussionmentioning

confidence: 99%

Two‐Particle Self‐Consistent Method for the Multi‐Orbital Hubbard Model

2021

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“…In addition, recently, computational techniques using the compact IR basis have been developed to calculate the dynamic susceptibility [32][33][34]. It is expected that by using the basis obtained by SpM-Padé, the accuracy of these analytic calculations will be improved.…”

Section: Discussionmentioning

confidence: 99%

Robust analytic continuation combining the advantages of the sparse modeling approach and Padé approximation

Motoyama,

Yoshimi,

Otsuki

2021

Preprint

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Analytic continuation (AC) from the imaginary-time Green's function to the spectral function is a crucial process for numerical studies of the dynamical properties of quantum many-body systems. This process, however, is an ill-posed problem; that is, the obtained spectrum is unstable against the noise of the Green's function. Though several numerical methods have been developed, each of them has its own advantages and disadvantages. The sparse modeling (SpM) AC method, for example, is robust against the noise of the Green's function but suffers from unphysical oscillations in the lowenergy region. We propose a new method that combines the SpM AC with the Padé approximation. This combination, called SpM-Padé, inherits robustness against noise from SpM and low-energy accuracy from Padé, compensating for the disadvantages of each. We demonstrate that the SpM-Padé method yields low-variance and low-biased results with almost the same computational cost as that of the SpM method.

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“…as an approximation of G. Here, g, g ∈ R r . Although it is tempting to compare (22) with (17) and assume G DLR ≈ G holds to high accuracy, this is not guaranteed a priori. Indeed, if the interpolation nodes τ k were not selected carefully, this would not be the case.…”

Section: The Imaginary Time Dlr Gridmentioning

confidence: 99%

“…In Refs. 10 and 13, orthogonal bases for imaginary time Green's functions containing only O (log Λ) basis functions are constructed from the left singular vectors in the singular value decomposition (SVD) of a discretization of K. This method, called the intermediate representation (IR), has been used successfully in a variety of applications, including those involving two-particle quantities 4,5,[14][15][16][17][18] ; see also Ref. 19 for a useful review and further references.…”

Section: Introductionmentioning

confidence: 99%

Discrete Lehmann representation of imaginary time Green's functions

Kaye,

Chen,

Parcollet

2021

Preprint

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Efficient ab initio Migdal-Eliashberg calculation considering the retardation effect in phonon-mediated superconductors

Cited by 31 publications

References 40 publications

Two‐Particle Self‐Consistent Method for the Multi‐Orbital Hubbard Model

Two‐Particle Self‐Consistent Method for the Multi‐Orbital Hubbard Model

Robust analytic continuation combining the advantages of the sparse modeling approach and Padé approximation

Discrete Lehmann representation of imaginary time Green's functions

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