Cluster approach study of intersite electron correlations in pyrochlore and checkerboard lattices

TL;DR

This study investigates electron correlations in pyrochlore and checkerboard lattices using an extended Hubbard model with a focus on short-range Coulomb interactions, revealing a kinetic energy reduction near a critical interaction strength that may explain heavy fermion behavior.

Contribution

It develops a cluster variational approach to analyze short-range electron correlations in geometrically frustrated lattices at infinite on-site repulsion, providing analytical insights into ground state energy behavior.

Findings

Kinetic energy decreases significantly as Coulomb repulsion approaches a critical value.

The model's results are applicable to understanding heavy fermion behavior in LiV$_2$O$_4$.

Analytical expression for ground state energy in the quarter band filling case.

Abstract

To treat effects of electron correlations in geometrically frustrated pyrochlore and checkerboard lattices, an extended single-orbital Hubbard model with nearest neighbor hopping $\sim t$ and Coulomb repulsion $\sim V$ is applied. Infinite on-site repulsion, $U\to\infty$, is assumed, thus double occupancies of sites are forbidden completely in the present study. A variational Gutzwiller type approach is extended to examine correlations due to short-range $V-$interaction and a cluster approximation is developed to evaluate a variational ground state energy of the system. Obtained analytically in a special case of quarter band filling appropriate to LiV$_2$O$_4$, the resulting simple expression describes the ground state energy in the regime of intermediate and strong coupling $V$. Like in the Brinkman-Rice theory based on the standard Gutzwiller approach to the Hubbard model, the mean value of the kinetic energy is shown to be reduced strongly as the coupling $V$ approaches a critical value $V_{c}$. This finding may contribute to explaining the observed heavy fermion behavior in LiV$_2$O$_4$.