Phase diagram and spin correlations of the Kitaev-Heisenberg model: Importance of quantum effects

TL;DR

This paper investigates the phase diagram of the Kitaev-Heisenberg model on a honeycomb lattice, revealing how quantum effects influence the stability of various magnetic and spin-liquid phases through advanced computational methods.

Contribution

It combines exact diagonalization, cluster mean field, spin-wave, and perturbation theories to map out the phase diagram and analyze quantum spin-liquid phases in the model.

Findings

Four magnetically ordered phases identified: Néel, ferromagnetic, zigzag, and stripy.

Two disordered quantum spin-liquid phases found, with the ferromagnetic Kitaev spin liquid being particularly broad.

Spatial spin correlations and dynamic structure factors characterized across phase transitions.

Abstract

We explore the phase diagram of the Kitaev-Heisenberg model with nearest neighbor interactions on the honeycomb lattice using the exact diagonalization of finite systems combined with the cluster mean field approximation, and supplemented by the insights from the linear spin-wave and second--order perturbation theories. This study confirms that by varying the balance between the Heisenberg and Kitaev term, frustrated exchange interactions stabilize in this model four phases with magnetic long range order: N\'eel phase, ferromagnetic phase, and two other phases with coexisting antiferromagnetic and ferromagnetic bonds, zigzag and stripy phases. They are separated by two disordered quantum spin-liquid phases, and the one with ferromagnetic Kitaev interactions has a substantially broader range of stability as the neighboring competing ordered phases, ferromagnetic and stripy, have very weak quantum fluctuations. Focusing on the quantum spin-liquid phases, we study spatial spin correlations and dynamic spin structure factor of the model by the exact diagonalization technique, and discuss the evolution of gapped low-energy spin response across the quantum phase transitions between the disordered spin liquid and magnetic phases with long range order.