Extremely Correlated Fermi Liquids in the limit of infinite dimensions

Abstract

We study the infinite spatial dimensionality limit of the recently developed Extremely Correlated Fermi Liquid (ECFL) theory for the t-J model. We directly analyze the Schwinger equations of motion for the Gutzwiller projected electron Green's function. From simplifications arising in this limit, we are able to make several exact statements about the theory. The ECFL Green's function is shown to have a momentum independent Dyson (Mori) self energy. For practical calculations we introduce a partial projection parameter λ, and obtain the complete set of ECFL integral equations to second order in λ. In a related publication, these equations are compared in detail with the dynamical mean field theory for the large U Hubbard model. Paralleling the well known mapping for the Hubbard model, we find that the infinite dimensional t-J model can be mapped to the infinite-U Anderson impurity model with a self-consistently determined set of parameters. This mapping extends individually to the auxiliary Green's function and the caparison factor of the ECFL theory. Additionally, the optical conductivity is shown to be obtainable from the Green's function with negligibly small vertex corrections. These results are shown to hold to each order in λ.

13 pages, 0 figures, To be published in "Annals of Physics" (2013)

References in corpus (4)

• How bad metals turn good: spectroscopic signatures of resilient quasiparticles
• Extremely Correlated Fermi Liquids
• Extremely Correlated Fermi Liquid Description of Normal State ARPES in Cuprates
• Extremely Correlated Fermi Liquids: The Formalism

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• Low energy physics of the t-J model in $d=\infty$ using Extremely Correlated Fermi Liquid theory: Cutoff Second Order Equations
• Extremely Correlated Fermi Liquid study of the U=infinity Anderson Impurity Model
• Theory of extreme correlations using canonical Fermions and path integrals
• Damping of spinful excitons in LaCoO${}_3$ by thermal fluctuations: Theory and experiment
• Linked-cluster expansion for the Green's function of the infinite-U Hubbard model
• Diagrammatic $\lambda$ series for extremely correlated Fermi liquids
• The splitting of electrons and violation of the Luttinger sum rule
• Nonresonant Raman Scattering in Extremely Correlated Fermi Liquids
• Extremely Correlated Fermi Liquid theory for $U=\infty$, $d=\infty$ Hubbard model to $\mathcal{O}({\lambda }^3)$