Variational study of the magnetization plateaus in the spin-1/2 kagome Heisenberg antiferromagnet: an approach from vision transformer neural quantum states

TL;DR

This study uses neural network-based variational wavefunctions to analyze the magnetization plateaus in the spin-1/2 kagome Heisenberg antiferromagnet, confirming several plateaus and revealing complex symmetry-breaking states.

Contribution

It introduces a neural network variational approach to accurately identify and characterize magnetization plateaus and their associated symmetry-breaking states in the kagome antiferromagnet.

Findings

Confirmed magnetization plateaus at 1/3, 5/9, and 7/9 saturation.

Identified competing valence bond crystal states at 1/9 plateau.

Predicted experimentally observable local magnetization modulations.

Abstract

We analyze the magnetization curve of the spin-1/2 kagome Heisenberg model in a magnetic field. Using state-of-the-art variational wavefunctions based on neural networks, we confirm the presence of robust magnetization plateaus at $m=1/3$, $5/9$ and $7/9$ of the saturation value, stabilized by a spontaneous symmetry breaking of lattice translations with a $\sqrt{3}\times \sqrt{3}$ unit cell. Regarding the more challenging $m=1/9$ plateau, we find two competing valence bond crystals depending on the system size, both breaking translation as well as point group symmetries and with a larger $3\times 3$ unit cell. Such quantum states with local modulations of the magnetization average values could be observed experimentally in the near future.