Extremely Correlated Fermi Liquid theory for $U=\mathrm{\infty }$, $d=\mathrm{\infty }$ Hubbard model to $\mathcal{O}({\lambda }^3)$

We present the $\mathcal{O}({\lambda }^3)$ results from the $\lambda$ expansion in the extremely correlated Fermi liquid theory applied to the infinite-dimensional $t$-$J$ model (with $J=0$), and compare the results with the earlier $\mathcal{O}({\lambda }^2)$ results as well as the results from the dynamical mean field theory. We focus attention on the $T$ dependence of the resistivity $\rho (T)$, the Dyson self energy, and the quasiparticle weight $Z$ at various densities. The comparison shows that all the methods display quadratic in T resistivity followed by a quasi-linear in T resistivity characterizing a strange metal, and gives an estimate of the different scales of these variables relative to the exact results.