Numerical study of magnetization plateaux in the spin-1/2 Heisenberg antiferromagnet on the checkerboard lattice

TL;DR

This study uses numerical methods to identify multiple magnetization plateaux in the spin-1/2 Heisenberg antiferromagnet on a checkerboard lattice, revealing complex valence-bond crystal phases that break lattice symmetries.

Contribution

It provides the first comprehensive numerical analysis of magnetization plateaux and associated valence-bond crystal phases in this model, expanding understanding of quantum magnetism.

Findings

Magnetization plateaux at m=0, 1/4, 1/2, 3/4 identified

Valence-bond crystal phases break lattice symmetries

Results supported by Exact Diagonalization and DMRG simulations

Abstract

We present numerical evidence that the spin-1/2 Heisenberg model on the two-dimensional checkerboard lattice exhibits several magnetization plateaux for m=0, 1/4, 1/2 and 3/4, where m is the magnetization normalized by its saturation value. These incompressible states correspond to somehow similar valence-bond crystal phases that break lattice symmetries, though they are different from the already established plaquette phase for m=0. Our results are based on Exact Diagonalization as well as Density Matrix Renormalization Group large-scale simulations, and interpreted in terms of simple trial wavefunctions.