From an antiferromagnet to a valence bond solid: evidence for a first-order phasetransition

Abstract

Using a loop–cluster algorithm we investigate the spin- Heisenberg antiferromagnet on a square lattice with exchange couplingJ and an additional four-spin interaction of strengthQ. We confirm the existence of a phase transition separating antiferromagnetism atJ/Q>Jc/Q from a valence bondsolid (VBS) state at J/Q<Jc/Q. Although our Monte Carlo data are consistent with those of previousstudies, we do not confirm the existence of a deconfined quantumcritical point. Instead, using a flowgram method on lattices as large as802, we find evidence for a weak first-order phase transition. Wealso present a detailed study of the antiferromagnetic phase. ForJ/Q>Jc/Q the staggered magnetization, the spin stiffness and the spinwave velocity of the antiferromagnetare determined by fitting Monte Carlo data to analytic results from the systematic low-energyeffective field theory for magnons. Finally, we also investigate the physics of the VBS state atJ/Q<Jc/Q and we show that long but finite antiferromagnetic correlations are still present.