| The Antiferromagnetic (AF) to Valence-Bond Solid (VBS) transition in two-dimensional spin systems is an interesting topic in condensed matter physics. This phase transition destroys long range spin correlations through quantum fluctuations at temperature T = 0. It has been more intensely studied since the theory of "deconfined" quantum critical points (DQCP) by Senthil et al. According to the "Landau rules", a direct transition breaking two unrelated symmetries should be generically first order. DQCP theory suggests, however, that this transition is generically continuous, and there is no coexistence of AF and VBS order. The transition point is instead characterized by deconfined S=1/2 spinons coupled to an emergent U(1) gauge field.;Various models with frustration have been studied, but "sign problems" hinder quantum Monte Carlo calculations. Here I study a "J-Q" model with four-spin interactions, which is a non-frustrating and isotropic quantum spin model that can realize an AF--VBS transition. However, the VBS order existing in it is relatively weak, and the broken lattice symmetry can not be observed easily. The true VBS ground state (as there are several possible candidate states with different ordering patterns) remains controversial. I also study two generalizations of the J-Q model: a J-Q 3 model with six-spin interactions, and J-Q models with SU( N) spins. An effective "pseudo hamiltonian" model is also discussed.;Carefully executed calculations of these models generate results compatible with the continuous phase transition scenario. The J-Q3 model is confirmed to be in the same universality class as the J-Q model. The SU( N), N = 3, 4, spins enhance the VBS order, and the critical exponents exhibit a systematic evolution for increasing N, in agreement with the N → infinity theoretical prediction by Sachdev et al.;In all studies of the generalized models, robust VBS order is observed, and the ground states are confirmed to be of the columnar VBS type. This enables us to investigate the Z4 (from the square lattice) to U(1) (predicted by DQCP theory) order parameter symmetry crossover inside the VBS phase. We discuss the new length scale Λ arising and governing the symmetry crossover.;Although a weakly first order transition can not be strictly ruled out, our results are in support of the DQCP theory. The models allow for the first time systematic study of the AF--VBS transition. |
