Antiferromagnetic to valence-bond-solid transitions in two-dimensional SU(N) Heisenberg models with multispin interactions

We study two-dimensional Heisenberg antiferromagnets with additional multispin interactions which can drive the system into a valence-bond-solid state. For standard SU(2) spins, we consider both four- and six-spin interactions. We find continuous quantum phase transitions with the same critical exponents. Extending the symmetry to SU(N), we also find continuous transitions for N=3 and 4. In addition, we also study quantitatively the crossover of the order-parameter symmetry from Z(4) deep inside the valence-bond-solid phase to U(1) as the phase transition is approached.