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

Understand

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.