Using the coupled cluster method we study the phase diagram of the spin-1/2 Heisenberg antiferromagnet on a honeycomb lattice with nearest-neighbour exchange coupling J1 > 0 and frustrating next-nearest-neighbour coupling J2 ≡ xJ1 > 0. In the range 0 < x < 1 we find four phases exhibiting respectively Néel, 6-spin plaquette, staggered dimer and Néel-II orderings, with quantum critical points at xc1 ≈ 0.207(3), xc2 ≈ 0.385(10) and xc3 ≈ 0.65(5). The transitions at xc1 and xc3 appear to be continuous (and hence deconfined) ones, while that at xc2 appears to be a direct first-order one.
Using the coupled cluster method we study the phase diagram of the spin-1/2 Heisenberg antiferromagnet on a honeycomb lattice with nearest-neighbour exchange coupling J1 > 0 and frustrating next-nearest-neighbour coupling J2 ≡ xJ1 > 0. In the range 0 < x < 1 we find four phases exhibiting respectively Néel, 6-spin plaquette, staggered dimer and Néel-II orderings, with quantum critical points at xc1 ≈ 0.207(3), xc2 ≈ 0.385(10) and xc3 ≈ 0.65(5). The transitions at xc1 and xc3 appear to be continuous (and hence deconfined) ones, while that at xc2 appears to be a direct first-order one.
The ground-state (GS) phase diagram of the frustrated spin- s J 1 -J 2 -J 3 Heisenberg antiferromagnet on the honeycomb lattice is studied using the coupled cluster method implemented to high orders of approximation, for spin quantum numbers s = 1, 3/2, 2 , 5/2. The model has antiferromagnetic (AFM) nearest-neighbour, next-nearest-neighbour and next-next-nearest-neighbour exchange couplings (with strength J 1 > 0, J 2 > 0 and J 3 > 0, respectively). We specifically study the case J 3 = J 2 = κJ 1 , in the range 0 < κ < 1 of the frustration parameter, which includes the point of maximum classical (s → ∞ ) frustration, viz., the classical critical point at κ cl = 1/2 , which separates the Neel phase for κ < κ cl and the collinear striped AFM phase for κ > κ cl . Results are presented for the GS energy, magnetic order parameter and plaquette valence-bond crystal (PVBC) susceptibility. For all spins s > 3/2 we find a quantum phase diagram very similar to the classical one, with a direct first-order transition between the two collinear AFM states at a value κ c (s) which is slightly greater than κ c l [e.g., κ c (3/2) ≈ 0.53(1)] and which approaches it monotonically as s → ∞ . By contrast, for the case s = 1 the transition is split into two such that the stable GS phases are one with Néel AFM order for κ < κ c1 = 0.485(5) and one with striped AFM order for κ > κ c2 = 0.528(5), just as in the case s = 1/2 (for which κ c1 ≈ 0.47 and κ c2 ≈ 0.60). For both the s = 1/2 and s = 1 models the transition at κ c2 appears to be of first-order type, while that at κ c1 appears to be continuous. However, whereas in the s = 1/2 case the intermediate phase appears to have PVBC order over the entire range κ c1 < κ < κ c2 , in the s = 1 case PVBC ordering either exists only over a very small part of the region or, more likely, is absent everywhere.
We study the ground-state (gs) phase diagram of the frustrated spin-21J1--J2--J3 antiferromagnet with ${J}_{2}={J}_{3}=\ensuremath{\kappa}{J}_{1}$ on the honeycomb lattice using coupled-cluster theory and exact diagonalization methods. We present results for the gs energy, magnetic order parameter, spin-spin correlation function, and plaquette valence-bond crystal (PVBC) susceptibility. We find a N\'eel antiferromagnetic (AFM) phase for $\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{1}}\ensuremath{\approx}0.47$, a collinear striped AFM phase for $\ensuremath{\kappa}>{\ensuremath{\kappa}}_{{c}_{2}}\ensuremath{\approx}0.60$, and a paramagnetic PVBC phase for ${\ensuremath{\kappa}}_{{c}_{1}}\ensuremath{\lesssim}\ensuremath{\kappa}\ensuremath{\lesssim}{\ensuremath{\kappa}}_{{c}_{2}}$. The transition at ${\ensuremath{\kappa}}_{{c}_{2}}$ appears to be of first-order type, while that at ${\ensuremath{\kappa}}_{{c}_{1}}$ is continuous. Since the N\'eel and PVBC phases break different symmetries our results favor the deconfinement scenario for the transition at ${\ensuremath{\kappa}}_{{c}_{1}}$.
We study the zero-temperature quantum phase diagram of a spin-1 Heisenberg antiferromagnet on the honeycomb lattice with both nearest-neighbor exchange coupling J1>0 and frustrating next-nearest-neighbor coupling ${J}_{2}\ensuremath{\equiv}\ensuremath{\kappa}{J}_{1}>0$, using the coupled cluster method implemented to high orders of approximation, and based on model states with different forms of classical magnetic order. For each we calculate directly in the bulk thermodynamic limit both ground-state low-energy parameters (including the energy per spin, magnetic order parameter, spin stiffness coefficient, and zero-field uniform transverse magnetic susceptibility) and their generalized susceptibilities to various forms of valence-bond crystalline (VBC) order, as well as the energy gap to the lowest-lying spin-triplet excitation. In the range $0<\ensuremath{\kappa}<1$ we find evidence for four distinct phases. Two of these are quasiclassical phases with antiferromagnetic long-range order, one with two-sublattice N\'eel order for $\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{1}}=0.250(5)$, and another with four-sublattice N\'eel-II order for $\ensuremath{\kappa}>{\ensuremath{\kappa}}_{{c}_{2}}=0.340(5)$. Two different paramagnetic phases are found to exist in the intermediate region. Over the range ${\ensuremath{\kappa}}_{{c}_{1}}<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{c}^{i}=0.305(5)$ we find a gapless phase with no discernible magnetic order, which is a strong candidate for being a quantum spin liquid, while over the range ${\ensuremath{\kappa}}_{c}^{i}<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{2}}$ we find a gapped phase, which is most likely a lattice nematic with staggered dimer VBC order that breaks the lattice rotational symmetry.
We present a comprehensive computational study of the phase diagram of the frustrated S=1/2 Heisenberg antiferromagnet on the honeycomb lattice, with second-nearest (J2) and third-neighbor (J3) couplings. Using a combination of exact diagonalizations (EDs) of the original spin model, of the Hamiltonian projected into the nearest-neighbor short-range valence-bond basis, and of an effective quantum dimer model, as well as a self-consistent cluster mean-field theory, we determine the boundaries of several magnetically ordered phases in the region ${J}_{2},{J}_{3}\ensuremath{\in}[0,1]$, and find a sizable magnetically disordered region in between. We characterize part of this magnetically disordered phase as a plaquette valence-bond crystal phase. At larger J2, we locate a sizable region in which staggered valence-bond crystal correlations are found to be important, either due to genuine valence-bond crystal (VBC) ordering or as a consequence of magnetically ordered phases, which break lattice rotational symmetry. Furthermore, we find that a particular parameter-free Gutzwiller projected tight-binding wave function has remarkably accurate energies compared to finite-size extrapolated ED energies along the transition line from conventional N\'eel to plaquette VBC phases, a fact that points to possibly interesting critical behavior---such as a deconfined critical point---across this transition. We also comment on the relevance of this spin model to model the spin liquid region found in the half filled Hubbard model on the honeycomb lattice.
We use the coupled-cluster method in high orders of approximation to make a comprehensive study of the ground-state (GS) phase diagram of the spin-1/2 J1-J2-J3 model on a two-dimensional honeycomb lattice with antiferromagnetic (AFM) interactions up to third-nearest neighbors. Results are presented for the GS energy and the average local onsite magnetization. With the nearest-neighbor coupling strength ${J}_{1}\ensuremath{\equiv}1$, we find four magnetically ordered phases in the parameter window ${J}_{2},{J}_{3}\ensuremath{\in}[0,1]$, namely, the N\'eel, striped, and N\'eel-II collinear AFM phases, plus a spiral phase. The N\'eel-II phase appears as a stable GS phase in the classical version of the model only for values J3<0. Each of these four ordered phases shares a boundary with a disordered quantum paramagnetic (QP) phase, and at several widely separated points on the phase boundaries the QP phase has an infinite susceptibility to plaquette valence-bond crystalline order. We identify all of the phase boundaries with good precision in the parameter window studied, and we find three tricritical quantum critical points therein at (a) $({J}_{2}^{{c}_{1}},{J}_{3}^{{c}_{1}})=(0.51\ifmmode\pm\else\textpm\fi{}0.01,0.69\ifmmode\pm\else\textpm\fi{}0.01)$ between the N\'eel, striped, and QP phases; (b) $({J}_{2}^{{c}_{2}},{J}_{3}^{{c}_{2}})=(0.65\ifmmode\pm\else\textpm\fi{}0.02,0.55\ifmmode\pm\else\textpm\fi{}0.01)$ between the striped, spiral, and QP phases; and (c) $({J}_{2}^{{c}_{3}},{J}_{3}^{{c}_{3}})=(0.69\ifmmode\pm\else\textpm\fi{}0.01,0.12\ifmmode\pm\else\textpm\fi{}0.01)$ between the spiral, N\'eel-II, and QP phases.
Using the density matrix renormalization group, we determine the phase diagram of the spin-1/2 Heisenberg antiferromagnet on a honeycomb lattice with a nearest-neighbor interaction J(1) and a frustrating, next-nearest-neighbor exchange J(2). As frustration increases, the ground state exhibits Néel, plaquette, and dimer orders, with critical points at J(2)/J(1) = 0.22 and 0.35. We observe that both the spin gap and the corresponding order parameters vanish continuously at both the critical points, indicating the presence of deconfined quantum criticality.