Frustrated Heisenberg antiferromagnet on the honeycomb lattice with spin quantum number $s\ge 1$

Abstract

The ground-state (GS) phase diagram of the frustrated spin-$s$ $J_1$--$J_2$--$J_3$ Heisenberg antiferromagnet on the honeycomb lattice is studied using the coupled cluster method, for spin quantum numbers $s=1,\frac{3}{2},2,\frac{5}{2}$. We study the case $J_3=J_2=\kappa J_1$, in the range $0\le \kappa \le 1$, which includes the point of maximum classical ($s\to \infty$) frustration, viz., the classical critical point at ${\kappa }_{\mathrm{cl}}=\frac{1}{2}$, separating the Néel phase for $\kappa <{\kappa }_{\mathrm{cl}}$ and the collinear striped AFM phase for $\kappa >{\kappa }_{\mathrm{cl}}$. Results are presented for the GS energy, magnetic order parameter and plaquette valence-bond crystal (PVBC) susceptibility. For all spins $s\ge \frac{3}{2}$ we find a quantum phase diagram very similar to the classical one, with a direct first-order transition between the two collinear AFM states at a value ${\kappa }_c(s)$ which is slightly greater than ${\kappa }_{\mathrm{cl}}$ [e.g., ${\kappa }_c(\frac{3}{2})\approx 0.53(1)$] and which approaches it monotonically as $s\to \infty$. By contrast, for the case $s=1$ the transition is split into two such that the stable GS phases are ones with Néel AFM order for $\kappa <{\kappa }_{c_1}=0.485(5)$ and with striped AFM order for $\kappa >{\kappa }_{c_2}=0.528(5)$, just as in the case $s=\frac{1}{2}$ (for which ${\kappa }_{c_1}\approx 0.47$ and ${\kappa }_{c_2}\approx 0.60$). For both the $s=\frac{1}{2}$ and $s=1$ models the transition at ${\kappa }_{c_2}$ appears to be of first-order type, while that at ${\kappa }_{c_1}$ appears to be continuous. However, whereas in the $s=\frac{1}{2}$ case the intermediate phase appears to have PVBC order over the entire range ${\kappa }_{c_1}<\kappa <{\kappa }_{c_2}$, in the $s=1$ case PVBC ordering either exists only over a very small part of the region or, more likely, is absent everywhere.

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• The Interplay Between Lattice Topology, Frustration, and Spin Quantum Number in Quantum Antiferromagnets on Archimedean Lattices
• A frustrated honeycomb-bilayer Heisenberg antiferromagnet: The spin-$\frac{1}{2}$ $J_1$--$J_2$--$J_1^{\perp }$ model
• A high-order study of the quantum critical behavior of a frustrated spin-$\frac{1}{2}$ antiferromagnet on a stacked honeycomb bilayer
• Multiple insulating phases due to the interplay of strong correlations and lattice geometry in a single-orbital Hubbard model
• Integer vs. half-integer spin on an approximate honeycomb lattice