Extremely correlated Fermi liquids in the limit of infinite dimensions Original Research Article

We study the infinite spatial dimensionality limit (image) of the recently developed Extremely Correlated Fermi Liquid (ECFL) theory (Shastry 2011, 2013) for the image model at image. We directly analyze the Schwinger equations of motion for the Gutzwiller projected (i.e. image) electron Green’s function image. From simplifications arising in this limit image, 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 image, and obtain the complete set of ECFL integral equations to image. In a related publication (Zitko et al. 2013) , these equations are compared in detail with the dynamical mean field theory for the large image Hubbard model. Paralleling the well known mapping for the Hubbard model, we find that the infinite dimensional image model (with image) can be mapped to the infinite-image Anderson impurity model with a self-consistently determined set of parameters. This mapping extends individually to the auxiliary Green’s function image and the caparison factor image. Additionally, the optical conductivity is shown to be obtainable from image with negligibly small vertex corrections. These results are shown to hold to each order in image.