Extremely correlated Fermi liquids in the limit of infinite dimensions

We study the infinite spatial dimensionality limit (d -> infinity) of the recently developed Extremely Correlated Fermi Liquid (ECFL) theory (Shastry 2011, 2013) [117,18] for the t-J model at J = 0. We directly analyze the Schwinger equations of motion for the Gutzwiller projected (i.e. U = infinity) electron Green's function 9,. From simplifications arising in this limit d -> infinity, 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 lambda, and obtain the complete set of ECFL integral equations to 0(lambda(2)). In a related publication (Zitko et al. 2013) [23], 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 (with J = 0) 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 g and the caparison factor mu. Additionally, the optical conductivity is shown to be obtainable from g with negligibly small vertex corrections. These results are shown to hold to each order in A. (C) 2013 Elsevier Inc. All rights reserved.