Quantum phase diagram of the spin-1 J1−J2 Heisenberg model on the honeycomb lattice

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.