Low-energy physics of thet−Jmodel ind=∞using extremely correlated Fermi liquid theory: Cutoff second-order equations

We present the results for the low-energy properties of the infinite-dimensional $t\text{\ensuremath{-}}J$ model with $J=0$, using $O({\ensuremath{\lambda}}²)$ equations of the extremely correlated Fermi liquid formalism. The parameter $\ensuremath{\lambda}\ensuremath{\in}[0,1]$ 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 $n\ensuremath{\lesssim}1$. It overcomes the limitation to low densities $n\ensuremath{\lesssim}0.7$ 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 $\ensuremath{\omega},T$ self-energy, and the resistivity are reported. These are quite close at all densities to the exact numerical results of the $U=\ensuremath{\infty}$ 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 nonvanishing $J$.