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 multi-spin 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 swathe 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 CP 1 (NCCP 1 ) theory of deconfined criticality, similar to what is observed on a square lattice. However, a surprising three-fold 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 four-fold 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.

Scaling dimensions of higher-charge monopoles at deconfined critical points

“…The positive value of y 3 indicates that the Néel-VBS transition on the honeycomb lattice should not be in this universality class, and would most likely be driven first order. Quantum MC results for such systems [20,32,33] have seen no clear evidence of a first-order transition, although a trend in this direction with increasing system size has been suggested [20]. Our results indicate that the true nature of this transition is indeed first order, but the small value of y 3 is consistent with critical behavior, described by the NCCP 1 universality class, over a range of length scales.…”

“…Even allowing for the large and unconventional finite-size effects in this system [7,13], it seems unlikely that y 3 would be more than very weakly irrelevant, which would mean that three-fold anisotropy should be visible over moderate length scales in the JQ model on the honeycomb lattice. Pujari et al [33] have recently reported evidence of such anisotropy at the critical point.…”

“…For the honeycomb lattice, the picture is less clear [20,32,33], and we therefore focus on the corresponding value of q = 3.…”

Quantum criticality with two length scales

“…Other models were therefore pursued. In the J-Q model [15], the Heisenberg exchange J between S = 1/2 spins is supplemented by a VBS-inducing four-spin term Q which is amenable to efficient quan-tum Monte Carlo (QMC) simulations [15,16,17,18,19,20,21,22,23]. Although many results for the J-Q model support the DQC scenario, it has not been possible to draw definite conclusions because of violations of expected scaling relations that affect many properties.…”

“…Other models were therefore pursued. In the J-Q model [15], the Heisenberg exchange J between S = 1/2 spins is supplemented by a VBS-inducing four-spin term Q which is amenable to efficient quan-1 tum Monte Carlo (QMC) simulations [15,16,17,18,19,20,21,22,23] Here we show that the DQC puzzle can be resolved based on a finite-size scaling Ansatz including the two divergent length scales of the theory-the standard correlation length ξ, which captures the growth of both order parameters (ξ Néel ∝ ξ VBS ), and a faster-diverging length ξ associated with the thickness of VBS domain walls and spinon confinement (the size of a spinon bound state). We show that, contrary to past assumptions, ξ can govern the finite-size scaling even of magnetic properties that are sensitive only to ξ in the thermodynamic limit.…”