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

Abstract

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.