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Low energy physics of the t-J model in $d=\infty$ using Extremely Correlated Fermi Liquid theory: Cutoff Second Order Equations

We present the results for the low energy properties of the infinite dimensional t-J model with $J=0$, using $O(λ^2)$ equations of the extremely correlated Fermi liquid formalism. The parameter $λ\in [0,1]$ is analogous to the inverse spin parameter $1/(2S)$ in quantum magnets. The present analytical scheme allows us to approach the physically most interesting regime near the Mott insulating state $n\lesssim 1$. It overcomes the limitation to low densities $n \lesssim .7$ of earlier calculations, by employing a variant of the skeleton graph expansion, and a high frequency cutoff that is essential for maintaining the known high-T entropy. The resulting quasiparticle weight $Z$, the low $ω,T $ self energy and the resistivity are reported. These are quite close at all densities to the exact numerical results of the $U=\infty$ Hubbard model, obtained using the dynamical mean field theory. The present calculation offers the advantage of generalizing to finite $T$ rather easily, and allows the visualization of the loss of coherence of Fermi liquid quasiparticles by raising $T$. The present scheme is generalizable to finite dimensions and a non vanishing $J$.