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

To examine the validity of the scenario of the deconfined critical phenomena[1], we carry out quantum Monte Carlo simulation for the SU($N$) generalization of the Heisenberg model with four-body and six-body interactions[2]. The quantum phase transition between the SU($N$) N\'eel 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 $y \equiv 1/\nu$ as the system size increases. We discuss the details of finite-size scaling analysis. [1] T. Senthil, A. Vishwanath, L. Balentz, S. Sachdev and M.P.A. Fisher, Science 303 (2004). [2] K. Harada, T. Suzuki, T. Okubo, H. Matsuo, J. Lou, H. Watanabe, S. Todo, and N. Kawashima, arXiv:1307.0501.