Valence Bond Crystal Ground State of the 1/9 Magnetization Plateau in the Spin-1/2 Kagome Lattice

TL;DR

This study identifies the type 1 valence bond crystal as the ground state of the 1/9 magnetization plateau in the spin-1/2 kagome lattice, using exact diagonalization and perturbation theory to confirm its stability.

Contribution

It demonstrates that the type 1 VBC state is the most stable ground state at the 1/9 plateau, supported by energy calculations and stability analysis.

Findings

Type 1 VBC has the lowest energy among considered distortions.

The type 1 VBC remains stable down to the undistorted kagome lattice.

Energy calculations agree within 3% between methods.

Abstract

We investigate the ground state of a spin-1/2 kagome antiferromagnet at the 1/9 magnetization plateau, focusing primarily on six types of valence bond crystal (VBC) distortions. Among six types of VBC distortions, type 1 consistently exhibits the lowest ground-state energy. Analysis of the second derivative of the energy with respect to the distortion strength $J_{\rm d}$ using exact diagonalization reveals that, as the system size approaches the thermodynamic limit, the type 1 VBC state remains stable down to $J_{\rm d} = 1$, corresponding to the undistorted kagome lattice. Perturbation theory further supports the stability of the type 1 VBC state, providing energy values that agree with exact diagonalization results within 3%. We also explore the possibility that other types of VBC distortions could become the ground state, but type 1 VBC still exhibited the lowest energy. These findings suggest that the ground state of the 1/9 plateau in the kagome lattice is the type 1 VBC state.