Hardcore bosons on checkerboard lattices near half filling: geometric frustration, vanishing charge order and fractional phase

TL;DR

This study investigates a spinless hardcore boson model on checkerboard lattices, revealing the absence of charge order at half filling and the emergence of fractional charge defects away from half filling, with implications for fractionalization and defect propagation.

Contribution

It provides the first detailed analysis of fractional charge defects and their correlations in a frustrated bosonic lattice model using Green function Monte Carlo methods.

Findings

Charge order vanishes at half filling in the thermodynamic limit.

Holes induce fractional charge defects of ±e/2.

Defect correlations depend on the ratio t/J, indicating fractionalization behavior.

Abstract

We study a spinless hardcore boson model on checkerboard lattices by Green function Monte Carlo method. At half filling, the ground state energy is obtained up to $28\times 28$ lattice and extrapolated to infinite size, the staggered pseudospin magnetization is found to vanish in the thermodynamic limit. Thus the $(\pi,\pi)$ charge order is absent in this system. Away from half filling, two defects induced by each hole (particle) may carry fractional charge ($\pm e/2$). For one hole case, we study how the defect-defect correlation changes with $t/J$, which is the ratio between the hopping integral and cyclic exchange, equals to $V/2t$ when $V\gg t$. Moreover, we argue that these fractional defects may propagate independently when the concentration of holes (or defects) is large enough.