Transitions to valence-bond solid order in a honeycomb lattice antiferromagnet.

We use quantum Monte Carlo methods to study the ground-state phase diagram of a S=1/2 honeycomb lattice magnet in which a nearest-neighbor antiferromagnetic exchange J (favoring Néel order) competes with two different multispin interaction terms: a six-spin interaction Q3 that favors columnar valence-bond solid (VBS) order, and a four-spin interaction Q2 that favors staggered VBS order. For Q3~Q2⪢J, we establish that the competition between the two different VBS orders stabilizes Néel order in a large swath of the phase diagram even when J is the smallest energy scale in the Hamiltonian. When Q3⪢(Q2,J) [Q2⪢(Q3,J)], this model exhibits at zero temperature phase transition from the Néel state to a columnar (staggered) VBS state. We establish that the Néel-columnar VBS transition is continuous for all values of Q2, and that critical properties along the entire phase boundary are well characterized by critical exponents and amplitudes of the noncompact CP1 (NCCP1) theory of deconfined criticality, similar to what is observed on a square lattice. However, a surprising threefold anisotropy of the phase of the VBS order parameter at criticality, whose presence was recently noted at the Q2=0 deconfined critical point, is seen to persist all along this phase boundary. We use a classical analogy to explore this by studying the critical point of a three-dimensional XY model with a fourfold anisotropy field which is known to be weakly irrelevant at the three-dimensional XY critical point. In this case, we again find that the critical anisotropy appears to saturate to a nonzero value over the range of sizes accessible to our simulations. [ABSTRACT FROM AUTHOR]