From an Antiferromagnet to a Valence Bond Solid: Evidence for a First Order Phase Transition

TL;DR

This study uses Monte Carlo simulations to investigate a quantum phase transition in a spin-1/2 Heisenberg antiferromagnet with four-spin interactions, providing evidence for a weak first order transition rather than a deconfined quantum critical point.

Contribution

It demonstrates that the phase transition between antiferromagnetic and valence bond solid states is weakly first order, challenging previous claims of a deconfined quantum critical point.

Findings

Confirmed the existence of a phase transition between AF and VBS states.

Found evidence for a weak first order phase transition.

Detailed analysis of AF phase properties such as magnetization and spin stiffness.

Abstract

Using a loop-cluster algorithm we investigate the spin 1/2 Heisenberg antiferromagnet on a square lattice with exchange coupling $J$ and an additional four-spin interaction of strength $Q$. We confirm the existence of a phase transition separating antiferromagnetism at $J/Q > J_c/Q$ from a valence bond solid (VBS) state at $J/Q < J_c/Q$. Although our Monte Carlo data are consistent with those of previous studies, we do not confirm the existence of a deconfined quantum critical point. Instead, using a flowgram method on lattices as large as $80^2$, we find evidence for a weak first order phase transition. We also present a detailed study of the antiferromagnetic phase. For $J/Q > J_c/Q$ the staggered magnetization, the spin stiffness, and the spinwave velocity of the antiferromagnet are determined by fitting Monte Carlo data to analytic results from the systematic low-energy effective field theory for magnons. Finally, we also investigate the physics of the VBS state at $J/Q < J_c/Q$, and we show that long but finite antiferromagnetic correlations are still present.