Néel-State to Valence-Bond-Solid Transition on the Honeycomb Lattice: Evidence for Deconfined Criticality

Abstract

We study a spin-1/2 SU (2) model on the honeycomb lattice with nearest-neighbor antiferromagnetic exchange J that favors Néel order, and competing 6-spin interactions Q which favor a valence bond solid (VBS) state in which the bond-energies order at the "columnar" wavevector K = (2π/3, −2π/3). We present quantum Monte-Carlo evidence for a direct continuous quantum phase transition between Néel and VBS states, with exponents and logarithmic violations of scaling consistent with those at analogous deconfined critical points on the square lattice. Although this strongly suggests a description in terms of deconfined criticality, the measured three-fold anisotropy of the phase of the VBS order parameter shows unusual near-marginal behaviour at the critical point. PACS numbers:Many interesting materials at low temperature appear to be on the verge of a quantum phase transition involving a qualitative change in the nature of the ground state [1]. When one of the two competing T = 0 phases spontaneously breaks a symmetry, the transition can be studied using a path integral representation with a Landau-Ginzburg action [2] written in terms of the order parameter that characterizes the broken symmetry phase [1]. If phases on two sides of the critical point break different symmetries, Landau-Ginzburg theory generically predicts a direct first-order transition or a two-step transition with an intermediate phase. However, this path integral description in terms of orderparameter variables can sometimes involve Berry phases in a non-trivial way [3][4][5]. The presence of Berry phases, which correspond to complex Boltzmann weights for the corresponding classical statistical mechanics problem in one higher dimension [1], can invalidate the conclusions reached by the Landau-Ginzburg approach.In some of these cases, it is useful[6] to think in terms of topological defects in one of the ordered states, and view the competing ordered state as being the result of the condensation of these topological defects -this description[6] makes sense only if the quantum numbers carried by defects in one phase match those of the order parameter variable in the other phase. Under certain conditions, this alternate "non-Landau" description generically predicts a direct continuous transition [7,8] between the two ordered states, in contrast to predictions of classical Landau-Ginzburg theory. Square lattice S = 1/2 antiferromagnets undergoing a transition from a ground state with non-zero Néel order parameter M s to a valence-bond solid (VBS) ordered state, in which the "bond-energies" (singlet projectors) P ij ≡ 1 4 − S i · S j on nearest-neighbour bonds ij in thex (ŷ) direction develop long-range order at the "columnar" wavevectors K 1 = (π, 0) (K 2 = (0, π)), provide the best-studied example of such "deconfined critical points" [7,8]. In this case, Z 4 vortices in the complex VBS order parameter Ψ carry a net spin S = 1/2 in their core, suggesting that the onset of Néel order can be studied using a CP 1 description of M s : M s = z * α σ αβ z β ...

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

“…Recent numerical studies of tractable model Hamiltonians provide a fairly consistent picture of a direct secondorder transition between the Néel and the columnar VBS states 28,43,44 , with numerical estimates of the anomalous exponents η N and η D , correlation length exponent ν, and universal scaling functions 44 all consistent, within errors, with the best estimates for the square-lattice transition. Further, slow drifts in spin stiffness analogous to the square lattice case, have also been observed at the putative critical point 43 . All this strongly suggests that the honeycomb lattice transition is also described by the NCCP 1 theory of deconfined criticality.…”

“…All this strongly suggests that the honeycomb lattice transition is also described by the NCCP 1 theory of deconfined criticality. However, our recent work has also identified an important new feature of the honeycomb lattice transition 43 : if the honeycomb lattice transition is indeed described by the NCCP 1 theory, 3-fold monopoles must be irrelevant at the NCCP 1 critical point. Since Ψ ∼ ψ, this would imply that three-fold anisotropy in the phase of the VBS order parameter ψ is irrelevant at criticality.…”

“…The deconfined quantum critical point for the model at Q 2 = 0 has been studied in our previous work 43 , as well as in Ref. 44.…”

“…This theory of deconfined criticality has motivated several numerical studies [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45] of model quantum Hamiltonians designed 9 to host a Néel-VBS columnar transition. In parallel work, other studies have tried to access the physics of deconfined criticality in three dimensional classical models [45][46][47][48][49][50][51][52][53][54][55] .…”

High-pressure magnetization and NMR studies of α−RuCl3

“…In particular, a magnetic valence-bond-crystal state may be formed, in which the lattice symmetry is (A) either spontaneously broken 40,41 or (B) explicitly broken under pressure. The large spin gap revealed in the 1/ 35 T 1 indicates that ground sate may belong to case (B), where the interactions explicitly break the C 3 symmetry.…”