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 N\'eel 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 ${Q}_{3}\ensuremath{\sim}{Q}_{2}\ensuremath{\gg}J$, we establish that the competition between the two different VBS orders stabilizes N\'eel order in a large swath of the phase diagram even when
J is the smallest energy scale in the Hamiltonian. When ${Q}_{3}\ensuremath{\gg}({Q}_{2},J)$ $\mathrm{[}{Q}_{2}\ensuremath{\gg}({Q}_{3},J)\text{]}$, this model exhibits at zero temperature phase transition from the N\'eel state to a columnar (staggered) VBS state. We establish that the N\'eel-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.
We study the quantum phase transition between the
Z2 spin liquid and valence bond solid (VBS) orders on a triangular lattice. With a fully isotropic triangular lattice, the transition from a columnar or resonating-plaquette VBS order can either be first order or there could be two transitions with an intermediate phase. If the transition splits into two, then the
Z2 spin liquid will first experience a first-order
q=3 Potts transition to a new nematic
Z2 spin liquid that breaks the $2\ensuremath{\pi}/3$ lattice rotation symmetry (but retain translation symmetry, unlike the VBS states). The second transition will then take this new nematic
Z2 spin liquid to a columnar or resonating-plaquette VBS state through a second-orderthree-dimensional (3D)
XY∗ transition. On a distorted triangular lattice, the degeneracy between some of the different columnar VBS orders is lifted, and the phase transition can reduce to a single 3D
XY∗ transition.
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 six-spin interactions Q that favor a valence-bond-solid (VBS) state in which the bond energies order at the "columnar" wave vector 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 threefold anisotropy of the phase of the VBS order parameter shows unusual near-marginal behavior at the critical point.
We consider the
S=1/2 Heisenberg model with nearest-neighbor interaction
J and an additional multispin interaction
Q3 on the square lattice. The
Q3 term consists of three bond-singlet projectors and is chosen to favor the formation of a valence-bond solid (VBS) where the valence bonds (singlet pairs) form a staggered pattern. The model exhibits a quantum phase transition from the N\'eel state to the VBS as a function of
Q3/J. We study the model using quantum Monte Carlo (stochastic series expansion) simulations. The N\'eel-VBS transition in this case is strongly first order in nature, in contrast to similar previously studied models with continuous transitions into columnar VBS states. The qualitatively different transitions illustrate the important role of an emerging
U(1) symmetry in the latter case, which is not possible in the present model due to the staggered VBS pattern (which does not allow local fluctuations necessary to rotate the local VBS order parameter).
We study the N\'eel to fourfold columnar valence bond solid (cVBS) quantum phase transition in a sign-free
S=1 square-lattice model. This is the same kind of transition that for
S=1/2 has been argued to realize the prototypical deconfined critical point. Extensive numerical simulations of the square-lattice
S=1/2 N\'eel-VBS transition have found consistency with the deconfined critical point scenario with no direct evidence for first-order behavior. In contrast to the
S=1/2 case, in our quantum Monte Carlo simulations for the
S=1 model, we present unambiguous evidence for a direct conventional first-order quantum phase transition. Classic signs of a first-order transition demonstrating coexistence including double-peaked histograms and switching behavior are observed. The sharp contrast from the
S=1/2 case is remarkable; we hypothesize that this is a striking demonstration of the role of the size of the quantum spin in the phase diagram of two-dimensional lattice models.
We propose quantum phase transitions beyond the Landau's paradigm of Sp(4) spin Heisenberg models on the triangular and square lattices motivated by the exact $\text{Sp}(4)\ensuremath{\simeq}\text{SO}(5)$ symmetry of spin-3/2 fermionic cold atomic system with only
s-wave scattering. On the triangular lattice, we study a phase transition between the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ spin ordered phase and a
Z2 spin liquid phase; this phase transition is described by an O(8) sigma model in terms of fractionalized spinon fields, with significant anomalous scaling dimensions of spin order parameters. On the square lattice, we propose a deconfined critical point between the Neel order and the valence bond solid (VBS) order, which is described by the CP(3) model, and the monopole effect of the compact U(1) gauge field is expected to be suppressed at the critical point.