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

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.

21 pages, 10 figures

References in corpus (9)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Scaling in the Fan of an Unconventional Quantum Critical Point
• Deconfined criticality, runaway flow in the two-component scalar electrodynamics and weak first-order superfluid-solid transitions
• Hole dynamics in an antiferromagnet across a deconfined quantum critical point
• First-order phase transition in easy-plane quantum antiferromagnets
• Quantum spin nematics, dimerization, and deconfined criticality in quasi-one dimensional spin-1 magnets
• Monte Carlo Simulations of Quantum Spin Systems in the Valence Bond Basis

Cited by in corpus (9)

• Quantum magnetism and criticality
• Evidence of Unconventional Universality Class in a Two-Dimensional Dimerized Quantum Heisenberg Model
• Coulomb gas transitions in three-dimensional classical dimer models
• Paired electron pockets in the hole-doped cuprates
• Large-N estimates of universal amplitudes of the CP^{N-1} theory and comparison with the JQ model
• Quantum Phase Transition in the Four-Spin Exchange Antiferromagnet
• Deconfinement criticality for the spatially anisotropic triangular antiferromagnet with the ring exchange
• Deconfined quantum criticality driven by Dirac fermions in SU(2) antiferromagnets
• Universal properties of the U(1) current at deconfined quantum critical points: comparison with predictions from gauge/gravity duality