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

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 $J_{3}=J_{2}=κJ_{1}$, in the range $0 \leq κ\leq 1$, which includes the point of maximum classical ($s \to \infty$) frustration, viz., the classical critical point at $κ_{\rm cl}=\frac{1}{2}$, separating the Néel phase for $κ< κ_{\rm cl}$ and the collinear striped AFM phase for $κ> κ_{\rm cl}$. Results are presented for the GS energy, magnetic order parameter and plaquette valence-bond crystal (PVBC) susceptibility. For all spins $s \geq \frac{3}{2}$ 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 $κ_{c}(s)$ which is slightly greater than $κ_{\rm cl}$ [e.g., $κ_{c}(\frac{3}{2}) \approx 0.53(1)$] 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 $κ< κ_{c_{1}} = 0.485(5)$ and with striped AFM order for $κ> κ_{c_{2}} = 0.528(5)$, just as in the case $s=\frac{1}{2}$ (for which $κ_{c_{1}} \approx 0.47$ and $κ_{c_{2}} \approx 0.60$). For both the $s=\frac{1}{2}$ and $s=1$ models the transition at $κ_{c_{2}}$ appears to be of first-order type, while that at $κ_{c_{1}}$ 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 $κ_{c_{1}} < κ< κ_{c_{2}}$, in the $s=1$ case PVBC ordering either exists only over a very small part of the region or, more likely, is absent everywhere.