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

TL;DR

This study maps the quantum phase diagram of the spin-1 J1-J2 Heisenberg model on the honeycomb lattice, revealing magnetic and non-magnetic phases, including a plaquette valence-bond order, using DMRG methods.

Contribution

First detailed DMRG analysis of the spin-1 J1-J2 honeycomb model identifying multiple quantum phases and a non-magnetic plaquette phase.

Findings

Identified Néel and stripe antiferromagnetic phases.

Discovered a non-magnetic plaquette valence-bond phase.

Provided evidence for the stability of the plaquette phase in the thermodynamic limit.

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 ($0.0 \leq J_2/J_1 \leq 0.5$) by means of density matrix renormalization group (DMRG). In the parameter regime $J_2/J_1 \lesssim 0.27$, the system sustains a N\'{e}el 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.