From an antiferromagnet to a valence bond solid: Evidence for a first-order phase transition

F. J. Jiang*, M. Nyfeler, S. Chandrasekharan, U. J. Wiese

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

110 Citations (Scopus)


Using a loop-cluster algorithm we investigate the spin- 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>Jc/Q from a valence bond solid (VBS) state at J/Q<Jc/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 802, we find evidence for a weak first-order phase transition. We also present a detailed study of the antiferromagnetic phase. For J/Q>Jc/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<Jc/Q and we show that long but finite antiferromagnetic correlations are still present.

Original languageEnglish
Article numberP02009
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number2
Publication statusPublished - 2008 Feb 1
Externally publishedYes


  • Quantum Monte Carlo simulations
  • Quantum phase transitions (theory)

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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