The plaquette valence bond solid (VBS) phase of the
J1−J2 antiferromagnetic (AFM) Heisenberg honeycomb model has been studied using plaquette operator theory. Considering six
S=21 spins on a single plaquette the plaquette operator representation for the spin operators in terms of plaquette-singlet and plaquette-triplet boson operators has been developed. The formalism has been applied to the
J1−J2 honeycomb antiferromagnet to derive an effective interacting boson model in terms of those singlets and triplets. The effective model has been analyzed within the harmonic approximation and results have been compared with the exact diagonalization data. The evolution of Dirac and Weyl nodes with respect to
J2/J1 for this model has been studied.
We study the plaquette valence-bond solid phase of the spin-
1/2J1-
J2 antiferromagnet Heisenberg model on the square lattice within the bond-operator theory. We start by considering four
S=1/2 spins on a single plaquette and determine the bond operator representation for the spin operators in terms of singlet, triplet, and quintet boson operators. The formalism is then applied to the
J1-
J2 model and an effective interacting boson model in terms of singlets and triplets is derived. The effective model is analyzed within the harmonic approximation and the previous results of Zhitomirsky and Ueda [Phys. Rev. B 54, 9007 (1996)] are recovered. By perturbatively including cubic (triplet-triplet-triplet and singlet-triplet-triplet) and quartic interactions, we find that the plaquette valence-bond solid phase is stable within the parameter region
0.34<J2/J1<0.59, which is narrower than the harmonic one. Differently from the harmonic approximation, the excitation gap vanishes at both critical couplings
J2=0.34J1 and
J2=0.59J1. Interestingly, for
J2<0.48J1, the excitation gap corresponds to a singlet-triplet excitation at the $\ensuremath{\Gamma}$ point while, for
J2>0.48J1, it is related to a singlet-singlet excitation at the $\mathbf{X}=(\ensuremath{\pi}/2,0)$ point of the tetramerized Brillouin zone.
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 study an S = 1/2 Heisenberg model on the honeycomb lattice with first and second neighbor antiferromagnetic exchange (J(1)-J(2) model), employing exact diagonalization in both the S(z) = 0 basis and nearest neighbor singlet valence bond (NNVB) basis. We find that for 0.2 < J(2)/J(1) < 0.3, the NNVB basis gives a proper description of the ground state in comparison with the exact results. By analyzing the dimer-dimer as well as the plaquette-plaquette correlations and also defining appropriate structure factors, we investigate possible symmetry breaking states as the candidates for the ground state in the frustrated region. We provide a body of evidence in favor of plaquette valence bond ordering for 0.2 < J(2)/J(1) < 0.3. By further increasing the ratio J(2)/J(1), this state undergoes a transition to the staggered dimerized state.
We study the proposed plaquette resonating valence bond (pRVB) state in the honeycomb lattice ${J}_{1}\ensuremath{-}{J}_{2}$ model with frustration arising from next-nearest-neighbor interactions. Starting with the limit of decoupled hexagons, we develop a plaquette operator approach to describe the pRVB state and its low-energy excitations. Our calculation clarifies that the putative pRVB state necessarily has
f-wave symmetry: the plaquette wave function is an antisymmetric combination of the Kekul\'e structures. We estimate the plaquette ordering amplitude, ground-state energy, and spin gap as a function of
J2/J1. The pRVB state is most stable around ${J}_{2}/{J}_{1}\ensuremath{\sim}0.25$. We identify the wave vectors of the lowest triplet excitations, which can be verified using exact diagonalization or density-matrix renormalization group (DMRG) studies. When
J2 is reduced, we can have either a deconfined quantum phase transition (QPT) or a first-order transition into a N\'eel state. When
J2 is increased, we surmise that the system will undergo a first-order phase transition into a state which breaks lattice rotational symmetry.
We study the ground-state (gs) phase diagram of the frustrated spin-
21 J1--
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 ${\ensuremath{\kappa}}_{{c}_{1}}$.