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 Neel order) competes with two different multispin interaction terms: a six-spin interaction Q(3) that favors columnar valence-bond solid (VBS) order, and a four-spin interaction Q(2) that favors staggered VBS order. For Q(3) similar to Q(2) >> J, we establish that the competition between the two different VBS orders stabilizes Neel order in a large swath of the phase diagram even when J is the smallest energy scale in the Hamiltonian. When Q(3) >> (Q(2), J) [Q(2) >> (Q(3), J)], this model exhibits at zero temperature phase transition from the Neel state to a columnar (staggered) VBS state. We establish that the Neel-columnar VBS transition is continuous for all values of Q(2), 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 Q(2) = 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.