High order λ expansion in the t-J model using Extremely Correlated Fermi Liquid theory.

The results of the λ expansion for the Green's function in the t-J model to high orders are reported in two and infinite spatial dimensions. This expansion is defined through the Schwinger equation of motion, in which (0≤λ≤1) provides continuity between the Fermi gas and the fully correlated model. In recent work, we have formulated a systematic set of rules for the "Schwinger diagrams" which arise from this expansion. These include a set of standard Feynman diagrams, in which the band dispersion ε_k, and the superexchange J_k, play the role of the interaction, as well as a set of "Meta-Feynman" diagrams. The earlier λ expansion results, taken to second order, reliably reproduce the low-frequency part of the spectral function (in the immediate vicinity of the quasiparticle). The results of the higher order diagrams display a marked improvement in the features at high energies.