Quantum phase transitions around the staggered valence-bond solid

Motivated by recent numerical results, we study the quantum phase transitions between Z(2) spin-liquid, Neel-ordered, and various valence-bond solid (VBS) states on the honeycomb and square lattices, with emphasis on the staggered VBS. In contrast to the well-understood columnar VBS order, the staggered VBS is not described by an XY-order parameter with Z(N) anisotropy close to these quantum phase transitions. Instead, we demonstrate that on the honeycomb lattice, the staggered VBS is more appropriately described as an O(3)-or CP(2)-order parameter with cubic anisotropy, while on the square lattice it is described by an O(4)-or CP(3)-order parameter.