Charge degrees in the quarter-filled checkerboard lattice

TL;DR

This paper investigates charge behavior in a frustrated lattice system of spinless fermions at quarter-filling, deriving an effective Hamiltonian and mapping it to a gauge theory to understand charge degrees of freedom.

Contribution

It introduces an effective Hamiltonian for spinless fermions on a checkerboard lattice in the strong interaction limit and maps the model to a U(1) lattice gauge theory.

Findings

Effective ring exchange Hamiltonian derived for |t| << V

Model mapped to a confining U(1) lattice gauge theory

Provides a framework for understanding charge degrees in frustrated lattices

Abstract

For a systematic study of charge degrees of freedom in lattices with geometric frustration, we consider spinless fermions on the checkerboard lattice with nearest-neighbor hopping $t$ and nearest-neighbor repulsion $V$ at quarter-filling. An effective Hamiltonian for the limit $|t|\ll V$ is given to lowest non-vanishing order by the ring exchange ($\sim t^{3}/V^{2}$). We show that the system can equivalently be described by hard-core bosons and map the model to a confining U(1) lattice gauge theory.