The victory project v1.0: An efficient parquet equations solver

Li, Gang; Kauch, Anna; Pudleiner, Petra; Held, Karsten

doi:10.1016/j.cpc.2019.03.008

Cited by 37 publications

(43 citation statements)

References 24 publications

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“…This is also in sharp contrast to any ladder approximation where only a set of a priori chosen ladder diagrams are considered in favor of only certain type of fluctuations. More details about the parquet approach can be found in references [40][41][42][43][44][45][46][47][48][49][50][51] . Here we would like to concentrate on the extension of it to the EHM.…”

Section: Method: Parquet Approximation To the Ehmmentioning

confidence: 99%

“…The precise transition boundary is not of the prime interest of this work, instead we want to show how the transition is approached and how it is probed in the parquet approach, which is also of interest to many other cluster methods that have the access to the two-particle vertex functions. This work also represents a methodological progress which further extends the victory solver of the parquet equations [40][41][42] to include the non-local Coulomb interactions in a lattice model.…”

Section: Introductionmentioning

confidence: 99%

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Competition between antiferromagnetic and charge density wave fluctuations in the extended Hubbard model

et al. 2019

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By extending our victory implementation of the parquet approach to include non-local Coulomb interactions, we study the extended Hubbard model on the two-dimensional square lattice with a particular focus on the competition of the non-local charge and spin fluctuations. Surprisingly, we find that their competition, as the mechanism driving the phase transition towards the charge density wave, dominates only in a very narrow parameter regime in the immediate vicinity of the phase transition. Due to the special geometry and the Fermi surface topology of the square lattice, antiferromagnetic fluctuations dominate even for sizable next-nearest neighbor interactions. Our conclusions are based on the consistent observations in both the single-and twoparticle quantities, including the self-energy, the single-particle spectral function, the two-particle susceptibility, the density-density vertex function and the optical conductivity. Our work unbiasedly establishes the connection of these quantities to the charge fluctuations, and the way of interpretation can be readily applied to any many-body method with access to the two-particle vertex. arXiv:1905.03065v2 [cond-mat.str-el]

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Section: Method: Parquet Approximation To the Ehmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Competition between antiferromagnetic and charge density wave fluctuations in the extended Hubbard model

et al. 2019

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“…The traditional formulation of diagrammatic theories based on two-particle quantities poses however significant challenges. One of them is the immense algorithmic complexity of the parquet equations [13], which re-stricts direct numerical applications to impurity models [9,10,12,14] and small clusters [15][16][17][18][19][20]. Furthermore, the perturbation theory based on the two-particle self-energy has revealed fundamental problems which have received much attention in the context of nonperturbative approaches, such as the dynamical meanfield theory (DMFT) [3].…”

Section: Introductionmentioning

confidence: 99%

Single-boson exchange decomposition of the vertex function

2019

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We present a decomposition of the two-particle vertex function of the single-band Anderson impurity model which imparts a physical interpretation of the vertex in terms of the exchange of bosons of three flavors. We evaluate the various components of the vertex for an impurity model corresponding to the half-filled Hubbard model within dynamical mean-field theory. For small values of the interaction almost the entire information encoded in the vertex function corresponds to single-boson exchange processes, which can be represented in terms of the Hedin three-leg vertex and the screened interaction. Also for larger interaction, the single-boson exchange still captures scatterings between electrons and the dominant low-energy fluctuations and provides a unified description of the vertex asymptotics. The proposed decomposition of the vertex does not require the matrix inversion of the Bethe-Salpeter equation. Therefore, it represents a computationally lighter and hence more practical alternative to the parquet decomposition. arXiv:1907.03581v1 [cond-mat.str-el]

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“…A state-of-the-art implementation is available in the recent victory release. 41 This package is an efficient parquet solver for electron systems in one or two dimensions, which properly takes the high-frequency asymptotics into account via so-called kernel functions. 32,53 While the parquet equations are an exact set of equations, they require the fully irreducible two-particle vertex Λ as an input.…”

Section: Method: Extending Victory To Treat Non-local Interactionsmentioning

confidence: 99%

“…These terms are actually evaluated as a difference and in imaginary time, see Ref. 41. A similar regularization (extension to high frequencies) is employed for the Dyson-Schwinger equation (2).…”

Section: Method: Extending Victory To Treat Non-local Interactionsmentioning

confidence: 99%

Parquet approximation for molecules: Spectrum and optical conductivity of the Pariser-Parr-Pople model

et al. 2019

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We study a simple model system for the conjugated π-bonds in benzene, the Pariser-Parr-Pople (PPP) model, within the parquet approximation (PA), exemplifying the prospects of the PA for molecules. Advantages of the PA are its polynomial scaling with the number of orbitals, and the natural calculation of one-and two-particle spectral functions as well as of response and correlation functions. We find large differences in the electronic correlations in the PPP model compared to a Hubbard model with only local interactions. The quasiparticle renormalization (or mass enhancement) is much weaker in the PPP than in the Hubbard model, but the static part of the self-energy enhances the band gap of the former. Furthermore, the vertex corrections to the optical conductivity are much more important in the PPP model. Because non-local interactions strongly alter the self-energy, we conclude that the PA is more suitable for calculating conjugated π-bonds in molecules than single site dynamical mean-field theory.

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The victory project v1.0: An efficient parquet equations solver

Cited by 37 publications

References 24 publications

Competition between antiferromagnetic and charge density wave fluctuations in the extended Hubbard model

Competition between antiferromagnetic and charge density wave fluctuations in the extended Hubbard model

Single-boson exchange decomposition of the vertex function

Parquet approximation for molecules: Spectrum and optical conductivity of the Pariser-Parr-Pople model

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