We report on a valence bond projector Monte Carlo simulation of the cubic lattice quantum Heisenberg model with additional higher-order exchange interactions in each unit cell. The model supports two different valence bond solid (VBS) ground states. In one of these states, the dimer pattern is a three-dimensional analogue of the columnar pattern familiar from two dimensions. In the other, the dimers are regularly arranged along the four main diagonals in 1/8 of the unit cells. The phases are separated from one another and from a Néel phase by strongly first-order boundaries. Our results strengthen the case for exotic transitions in two dimensions, where no discontinuities have been detected at the Heisenberg Néel–VBS transition driven by four-spin plaquette interactions.

@article{
  title = {Valence Bond Solid Phases in a Cubic Antiferromagnet},
  author = {Beach, K. S. D. and Sandvik, Anders W.},
  journal = {Physical Review Letters},
  volume = {99},
  issue = {4},
  pages = {047202},
  numpages = {4},
  year = {2007},
  month = {Jul},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.99.047202},
  url = {http://link.aps.org/doi/10.1103/PhysRevLett.99.047202}
}