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

TL;DR

This paper analyzes the low energy properties of the infinite dimensional t-J model at zero J using an advanced correlated Fermi liquid approach, extending previous low-density limitations and aligning well with numerical results.

Contribution

It introduces a novel analytical scheme employing a cutoff and skeleton expansion to study the t-J model near the Mott insulator, applicable at finite temperatures and potentially in finite dimensions.

Findings

Quasiparticle weight Z closely matches numerical results

Resistivity and self-energy behaviors are accurately captured

Method overcomes low-density limitations of earlier approaches

Abstract

We present the results for the low energy properties of the infinite dimensional t-J model with $J=0$, using $O(\lambda^2)$ equations of the extremely correlated Fermi liquid formalism. The parameter $\lambda \in [0,1]$ 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 $\omega,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 $J$.