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arXiv:1303.2818

Dynamical Screening Effect on Local Two-Particle Vertex Functions

Li Huang, Yilin Wang

Published Mar 12, 2013• 0 citations
arXivHTMLPDF

Abstract

In principle, the electronic Coulomb interaction among the correlated orbitals is frequency-dependent. Though it is generally believed that the dynamically screened interaction may play a crucial role in understanding the subtle electronic structures of strongly correlated materials, hitherto we know very little about it. In the Letter, we demonstrate that within the framework of single-site dynamical mean-field theory the local two-particle Green's functions $χ$ and vertex functions $Γ$ are strongly modified by the dynamically screened interaction. Since both $χ$ and $Γ$ represent the main ingredients to compute momentum-resolved response functions and to treat non-local spatial correlations by means of diagrammatic extensions of dynamical mean-field theory, it is urgent to reexamine previous results by taking the dynamical screening effect into account. The modifications should be very considerable.

DOI
10.48550/arxiv.1303.2818

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In principle, the electronic Coulomb interaction among the correlated orbitals is frequency-dependent. Though it is generally believed that the dynamically screened interaction may play a crucial role in understanding the subtle electronic structures of strongly correlated materials, hitherto we know very little about it. In the Letter, we demonstrate that within the framework of single-site dynamical mean-field theory the local two-particle Green's functions χχχ and vertex functions ΓΓΓ are strongly modified by the dynamically screened interaction. Since both χχχ and ΓΓΓ represent the main ingredients to compute momentum-resolved response functions and to treat non-local spatial correlations by means of diagrammatic extensions of dynamical mean-field theory, it is urgent to reexamine previous results by taking the dynamical screening effect into account. The modifications should be very considerable.
Electronic-correlated systems are often well described by dynamical mean field theory (DMFT). While DMFT studies have mainly focused hitherto on one-particle properties, valuable information is also enclosed into local two-particle Green's functions and vertices. They represent the main ingredient to compute momentum-dependent response functions at the DMFT level and to treat nonlocal spatial correlations at all length scales by means of diagrammatic extensions of DMFT. The aim of this paper is to present a DMFT analysis of the local reducible and irreducible two-particle vertex functions for the Hubbard model in the context of a unified diagrammatic formalism. An interpretation of the observed frequency structures is also given in terms of perturbation theory, of the comparison with the atomic limit, and of the mapping onto the attractive Hubbard model.
Abstract The question of spatial locality of electronic correlations beyond GW approximation is one of the central issues of the famous combination of GW and dynamical mean field theory, GW + DMFT. In this work, the above question is addressed directly (for the first time) by performing calculations with and without assumption of locality of the corresponding diagrams. For this purpose we use sc(GW + G3W2) approach where the higher order part (G3W2) is evaluated with fully momentum dependent Green’s function G and screened interaction W and with ‘local’ variant, where the single site approximation is assumed for both G and W. For all three materials studied in this work (NiO, α -Ce, LiFeAs), we have found the spatial non-locality effects to be strong. For NiO and LiFeAs they, in fact, are decisive for the proper evaluation of vertex corrections. The results of this study have direct impact on our understanding of approximations made in practical implementations of GW + DMFT method, where all diagrams beyond GW (DMFT part) are assumed to be local. Taking into account the fact that the first diagrams beyond GW represent the most important contribution also in GW + DMFT calculations, we conclude that the basic assumption of GW + DMFT, namely the locality of diagrams evaluated in the DMFT part, is not as good as it is believed to be.
In the study of strongly interacting systems, correlations on the two-particle level are receiving more and more attention. In this work, we study a particular two-particle correlation function: the fermion-boson vertex. It describes the response of the Green's function when an external field is applied and is an important ingredient of diagrammatic extensions of dynamical mean-field theory. We provide several perspectives on this object, using Ward identities, sum rules, perturbative analysis, and asymptotic relations. We then use these tools to study the vertex across the doping-driven metal-insulator transition and find a divergent imaginary part.
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We present a fully self-consistent combined GW and dynamical mean field (DMFT) study of the extended two-dimensional Hubbard model. The inclusion of the local dynamical vertex stemming from the DMFT self-energy and polarization is shown to cure the known problems of self-consistent GW. We calculate momentum-resolved spectral functions, two-particle polarizations, and electron-loss spectra, as well as the effective dynamical interaction induced by nonlocal screening. The momentum-dependence introduced by GW into the extended DMFT description leads to a narrowing of the quasiparticle width and more pronounced Hubbard bands in the metallic regime as one approaches the charge-ordering transition. It further affects the shape of collective modes, giving rise to dispersive plasmon-like long-wavelength and stripe modes.
In the study of correlated systems, approximations based on the dynamical mean-field theory (DMFT) provide a practical way to take local vertex corrections into account, which capture, respectively, particle-particle screening at weak coupling and the formation of the local moment at strong coupling. We show that in both limits the local vertex corrections can be efficiently parametrized in terms of single-boson exchange, such that the two-particle physics described by DMFT and its diagrammatic extensions is recovered to good approximation and at a reduced computational cost. Our investigation highlights the importance of the frequency-dependent fermion-boson coupling (Hedin vertex) for local vertex corrections. Namely, at weak coupling the fermion--spin-boson coupling suppresses the N\'eel temperature of the DMFT approximation compared with the static mean field, whereas for large interaction it facilitates a huge enhancement of local spin-fluctuation exchange, giving rise to the effective-exchange energy scale 4t2/U4{t}^{2}/U4t2/U. We find that parametrizations of the vertex which neglect the nontrivial part of the fermion-boson coupling fail qualitatively at strong coupling.