Phase Diagram of the J1, J2, J3 Heisenberg Models on the Honeycomb Lattice: A Series Expansion Study

TL;DR

This study uses series expansions to analyze the phase diagram of the J1-J2-J3 Heisenberg model on the honeycomb lattice, revealing phase boundaries, magnetic orderings, and disordered regions with quantum effects.

Contribution

It introduces a series expansion approach around various magnetic states to map the phase diagram of the J1-J2-J3 honeycomb Heisenberg model, including quantum corrections.

Findings

First order transition between Ne9el and columnar states at large J3

Ne9el phase extends beyond classical stability region at J3=0

Large parameter regions stabilize spiral phases with renormalized angles

Abstract

We study magnetically ordered phases and their phase boundaries in the $J_1-J_2-J_3$ Heisenberg models on the honeycomb lattice using series expansions around N\'eel and different colinear and non-colinear magnetic states. An Ising anisotropy ($\lambda=J_{\perp}/J_z\ne 1$) is introduced and ground state energy and magnetization order parameter are calculated as a power seies expansion in $\lambda$. Series extrapolation methods are used to study properties for the Heisenberg model ($\lambda=1$). We find that at large $J_3$ ($>0.6$) there is a first order transition between N\'eel and columnar states, in agreement with the classical answer. For $J_3=0$, we find that the N\'eel phase extends beyond the region of classical stability. We also find that spiral phases are stabilized over large parameter regions, although their spiral angles can be substantially renormalized with respect to the classical values. Our study also shows a magnetically disordered region at intermedaite $J_2/J_1$ and $J_3/J_1$ values.