Quantum phase diagram of the spin-$1$ $J_1-J_2$ Heisenberg model on the honeycomb lattice

Abstract

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- ($J_1$) and second-neighbor ($J_2$) interactions ($0.0\le J_2/J_1\le 0.5$) by means of density matrix renormalization group (DMRG). In the parameter regime $J_2/J_1\lesssim 0.27$, the system sustains a Néel antiferromagnetic phase. At the large $J_2$ side $J_2/J_1\gtrsim 0.32$, a stripe antiferromagnetic phase is found. Between the two magnetic ordered phases $0.27\lesssim J_2/J_1\lesssim 0.32$, we find a \textit{non-magnetic} intermediate region with a plaquette valence-bond order. Although our calculations are limited within $6$ unit-cell width on cylinder, we present evidence that this plaquette state could be a strong candidate for this non-magnetic region in the thermodynamic limit. We also briefly discuss the nature of the quantum phase transitions in the system. We gain further insight of the non-magnetic phases in the spin-$1$ system by comparing its phase diagram with the spin-$1/2$ system.

7 pages, 10 figures

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