Extremely correlated Fermi liquids in the limit of infinite dimensions

• Infinite-dimensional tt–JJ model (J=0J=0) studied within new ECFL theory.
• Mapping to the infinite UU Anderson model with self consistent hybridization.
• Single particle Green’s function determined by two local self energies.
• Partial projection through control variable λλ.
• Expansion carried out to O(λ2)O(λ2) explicitly.

We study the infinite spatial dimensionality limit (d→∞d→∞) of the recently developed Extremely Correlated Fermi Liquid (ECFL) theory (Shastry 2011, 2013) [17] and [18] for the t–Jt–J  model at J=0J=0. We directly analyze the Schwinger equations of motion for the Gutzwiller projected (i.e. U=∞U=∞) electron Green’s function GG. From simplifications arising in this limit d→∞d→∞, 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 λλ, and obtain the complete set of ECFL integral equations to O(λ2)O(λ2). In a related publication (Zitko et al. 2013) [23], these equations are compared in detail with the dynamical mean field theory for the large UU Hubbard model. Paralleling the well known mapping for the Hubbard model, we find that the infinite dimensional t–Jt–J  model (with J=0J=0) can be mapped to the infinite-UU Anderson impurity model with a self-consistently determined set of parameters. This mapping extends individually to the auxiliary Green’s function g and the caparison factor μμ. Additionally, the optical conductivity is shown to be obtainable from GG with negligibly small vertex corrections. These results are shown to hold to each order in λλ.