Complete phase diagram of the spin-1/2 $J_{1}$-$J_{2}$-$J_{3}$ model (with $J_{3}=J_{2}$) on the honeycomb lattice

TL;DR

This study maps the complete zero-temperature ground-state phase diagram of the frustrated spin-1/2 $J_{1}$-$J_{2}$-$J_{3}$ model on the honeycomb lattice, revealing a direct first-order transition between Ne9el and ferromagnetic phases without intermediate states.

Contribution

The paper provides the first comprehensive phase diagram of the quantum $J_{1}$-$J_{2}$-$J_{3}$ honeycomb model with $J_{3}=J_{2}$ using the coupled cluster method, identifying the nature of phase transitions.

Findings

First-order transition at $J_{2}/J_{1} = -1.17 \, \pm \, 0.01$ for $J_{1}>0$

No evidence of intermediate phases between Ne9el and ferromagnetic states

Full zero-temperature ground-state phase diagram of the model presented

Abstract

We use the coupled cluster method to investigate the ground-state (GS) properties of the frustrated spin-1/2 $J_{1}$-$J_{2}$-$J_{3}$ model on the honeycomb lattice, with nearest-neighbor exchange coupling $J_1$ plus next-nearest-neighbor ($J_2$) and next-next-nearest-neighbor ($J_3$) exchanges of equal strength. In particular we find a direct first-order phase transition between the N\'eel-ordered antiferromagnetic phase and the ferromagnetic phase at a value $J_{2}/J_{1} = -1.17 \pm 0.01$ when $J_{1}>0$, compared to the corresponding classical value of -1. We find no evidence for any intermediate phase. From this and our previous CCM studies of the model we present its full zero-temperature GS phase diagram.