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 (20)

• "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
• Cluster Algorithm for Vertex Models
• Emergent Photons and New Transitions in the O(3) Sigma Model with Hedgehog Suppression
• Finite size and temperature effects in the AF Heisenberg model
• 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
• Ground state projection of quantum spin systems in the valence bond basis
• High-dimensional fractionalization and spinon deconfinement in pyrochlore antiferromagnets
• 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
• Weak first-order superfluid--solid quantum phase transitions
• Two-Dimensional Quantum XY Model with Ring Exchange and External Field
• Exact ground states of a frustrated 2D magnet: deconfined fractional excitations at a first order quantum phase transition
• Dimer-Quadrupolar Quantum Phase Transition in the Quasi-One-Dimensional Heisenberg Model with Biquadratic Interaction
• Frustrated Heisenberg antiferromagnets: fluctuation induced first order vs deconfined quantum criticality
• Theoretical constraints for the magnetic-dimer transition in two-dimensional spin models
• Monte Carlo Simulations of Quantum Spin Systems in the Valence Bond Basis

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