The frustrated Heisenberg antiferromagnet on the honeycomb lattice: $J_{1}$--$J_{2}$ model

TL;DR

This study maps the ground-state phases of the frustrated spin-1/2 $J_1$-$J_2$ honeycomb antiferromagnet, revealing a paramagnetic phase between two magnetic phases and characterizing the nature of phase transitions.

Contribution

It provides the first detailed coupled-cluster analysis of the $J_1$-$J_2$ honeycomb model, identifying the paramagnetic phase and the nature of phase transitions.

Findings

Identifies a paramagnetic PVBC phase between two magnetic phases.

Determines the critical points $\

and characterizes the phase transition types.

Abstract

We study the ground-state (gs) phase diagram of the frustrated spin-1/2 $J_{1}$--$J_{2}$ antiferromagnet with $J_{2}=\kappa J_1>0$ ($J_{1}>0$) on the honeycomb lattice, using the coupled-cluster method. We present results for the ground-state energy, magnetic order parameter and plaquette valence-bond crystal (PVBC) susceptibility. We find a paramagnetic PVBC phase for $\kappa_{c_1}<\kappa<\kappa_{c_2}$, where $\kappa_{c_1} \approx 0.207 \pm 0.003$ and $\kappa_{c_2} \approx 0.385 \pm 0.010$. The transition at $\kappa_{c_1}$ to the N\'{e}el phase seems to be a continuous deconfined transition (although we cannot exclude a very narrow intermediate phase in the range $0.21 \lesssim \kappa \lesssim 0.24$), while that at $\kappa_{c_2}$ is of first-order type to another quasiclassical antiferromagnetic phase that occurs in the classical version of the model only at the isolated and highly degenerate critical point $\kappa = 1/2$. The spiral phases that are present classically for all values $\kappa > 1/6$ are absent for all $\kappa \lesssim 1$.