Spin-$S\,$ Kitaev-Heisenberg model on the honeycomb lattice: A high-order treatment via the many-body coupled cluster method

TL;DR

This study applies the coupled cluster method to analyze the phase diagram of the spin-$S$ Kitaev-Heisenberg model on the honeycomb lattice, revealing accurate phase boundaries and unexpected narrow phases for different spin values.

Contribution

It demonstrates the effectiveness of the coupled cluster method in accurately determining phase boundaries and discovering new phases in the generalized Kitaev-Heisenberg model.

Findings

Accurate estimates of phase boundaries for spin liquid phases.

Identification of two unexpected narrow phases for S=1/2.

CCM captures strong quantum fluctuations in the model.

Abstract

We study the spin-$S$ Kitaev-Heisenberg model on the honeycomb lattice for $S\!=\!1/2$, $1$ and $3/2$, by using the coupled cluster method (CCM) of microscopic quantum many-body theory. This system is one of the earliest extensions of the Kitaev model and is believed to contain two extended spin liquid phases for any value of the spin quantum number $S$. We show that the CCM delivers accurate estimates for the phase boundaries of these spin liquid phases, as well as other transition points in the phase diagram. Moreover, we find evidence of two unexpected narrow phases for $S\!=\!1/2$, one sandwiched between the zigzag and ferromagnetic phases and the other between the N\'eel and the stripy phases. The results establish the CCM as a versatile numerical technique that can capture the strong quantum-mechanical fluctuations that are inherently present in generalized Kitaev models with competing bond-dependent anisotropies.