Strongly correlated electrons on frustrated lattices

TL;DR

This paper reviews recent research on charge excitations and magnetic phenomena in strongly correlated electrons on frustrated lattices, highlighting fractional charges, confinement, and new ferromagnetism mechanisms.

Contribution

It provides a comprehensive overview of fractional charge excitations, confinement phenomena, and novel ferromagnetism mechanisms in geometrically frustrated lattices.

Findings

Fractional charges $ ext{±}e/2$ can exist at specific fillings.

Fractional charges are confined in the checkerboard lattice.

A new kinetic mechanism for ferromagnetism on the kagome lattice.

Abstract

We give an overview of recent work on charge degrees of freedom of strongly correlated electrons on geometrically frustrated lattices. Special attention is paid to the checkerboard lattice, i.e., the two-dimensional version of a pyrochlore lattice and to the kagome lattice. For the checkerboard lattice it is shown that at half filling when spin degrees of freedom are neglected and quarter filling when they are included excitations with fractional charges $\pm$e/2 may exist. The same holds true for the three-dimensional pyrochlore lattice. In the former case the fractional charges are confined. The origin of the weak constant confining force is discussed and some similarities to quarks and to string theory are pointed out. For the checkerboard lattice a formulation in terms of a compact U(1) gauge theory is described. Furthermore a new kinetic mechanism for ferromagnetism at special fillings of a kagome lattice is discussed.