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Strongly correlated systems with geometric frustrations can host the emergent phases of matter with unconventional properties. Here, we study the spin S=1 Heisenberg model on the honeycomb lattice with the antiferromagnetic first-(J1) and second-neighbor (J2) interactions (0.0≤J2/J1≤0.5) by means of density-matrix renormalization group. In the parameter regime J2/J1≲0.27, the system sustains a Néel antiferromagnetic phase. At the large J2 side J2/J1≳0.32, a stripe antiferromagnetic phase is found. Between the two magnetic ordered phases 0.27≲J2/J1≲0.32, we find a nonmagnetic intermediate region with a plaquette valence-bond order. Although our calculations are limited within a six unit-cell width on cylinder, we present evidence that this plaquette state could be a strong candidate for this nonmagnetic region in the thermodynamic limit. We also briefly discuss the nature of the quantum phase transitions in the system. We gain further insight into the nonmagnetic phases in the spin-1 system by comparing its phase diagram with the spin-1/2 system. [ABSTRACT FROM AUTHOR]

We use the density matrix renormalization group (DMRG) algorithm to study the phase diagram of the spin-½ Heisenberg model on a honeycomb lattice with first (J1) and second (J2) neighbor antiferromagnetic interactions, where a Z2 spin liquid region has been proposed. By implementing SU(2) symmetry in the DMRG code, we are able to obtain accurate results for long cylinders with a width slightly over 15 lattice spacings and a torus up to the size N = 2 × 6 × 6. With increasing J2, we find a Néel phase with a vanishing spin gap and a plaquette valence-bond (PVB) phase with a nonzero spin gap. By extrapolating the square of the staggered magnetic moment ms² on finite-size cylinders to the thermodynamic limit, we find the Néel order vanishing at J2/J1 ≃ 0.22. For 0.25 < J2/J1 ⩽ 0.35, we find a possible PVB order, which shows a fast growing PVB decay length with increasing system width. For 0.22 < J2 < 0.25, both spin and dimer orders vanish in the thermodynamic limit, which is consistent with a possible spin liquid phase. We present calculations of the topological entanglement entropy, compare the DMRG results with the variational Monte Carlo, and discuss possible scenarios in the thermodynamic limit for this region. [ABSTRACT FROM AUTHOR]

A Kitaev-Heisenberg- J2-J3 model is proposed to describe the Mort-insulating layered iridates A2IrO3 (A = Na, Li). The model is a combination of the Kitaev honeycomb model and the Heisenberg model with all three nearest-neighbor couplings J1, J2, and J3. A rich phase diagram is obtained at the classical level, including the experimentally suggested zigzag ordered phase; as well as the stripy phase, which extends from the Kitaev-Heisenberg limit to the J1-J2-J3 one. Combining the experimentally observed spin order with the optimal fitting to the uniform magnetic susceptibility data gives an estimate of possible parameter values, which in turn reaffirms the necessity of including both the Kitaev and farther neighbor couplings. [ABSTRACT FROM AUTHOR]