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Possibility of Deconfined Criticality in SU(N) Heisenberg Models at Small N

To examine the validity of the scenario of the deconfined critical phenomena, we carry out a quantum Monte Carlo simulation for the SU($N$) generalization of the Heisenberg model with four-body and six-body interactions. The quantum phase transition between the SU($N$) Néel and valence-bond solid phases is characterized for $N=2,3,$ and $4$ on the square and honeycomb lattices. While finite-size scaling analysis works well up to the maximum lattice size ($L=256$) and indicates the continuous nature of the phase transition, a clear systematic change towards the first-order transition is observed in the estimates of the critical exponent $y \equiv 1/ν$ as the system size increases. We also confirm the relevance of a squared valence-bond solid field $Ψ^2$ for the SU(3) model.