### Abstract

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>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.

Original language | English |
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Article number | P02009 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2008 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2008 Feb 1 |

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### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

*Journal of Statistical Mechanics: Theory and Experiment*,

*2008*(2), [P02009]. https://doi.org/10.1088/1742-5468/2008/02/P02009