# Valence Bond Solid Phases in a Cubic Antiferromagnet

Journal Article

**Published:**Wednesday, July 25, 2007

**Citation:**Physical Review Letters, Volume 99, Number 47202, Pages 4

**Authors (2 total):** K. Beach,
A. W. Sandvik

**Abstract:** 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.