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We study two-dimensional Heisenberg antiferromagnets with additionalmulti-spin interactions which can drive the system into a valence-bond solidstate. For standard SU(2) spins, we consider both four- and six-spininteractions. We find continuous quantum phase transitions with the samecritical exponents. Extending the symmetry to SU(N), we also find continuoustransitions for N=3 and 4. In addition, we also study quantitatively thecross-over of the order-parameter symmetry from Z4 deep inside thevalence-bond-solid phase to U(1) as the phase transition is approached.

Antiferromagnetic to valence-bond-soild transitions in two-dimensional SU(N) Heisenberg models with multi-spin interactions