Quantum phase transitions in the Kitaev--Heisenberg model on a single hexagon

TL;DR

This paper investigates quantum phase transitions in a Kitaev--Heisenberg model on a hexagon, revealing how increasing Kitaev interactions induce transitions between different magnetic phases, with insights from exact diagonalization and cluster mean-field methods.

Contribution

It provides a detailed analysis of phase transitions in a finite Kitaev--Heisenberg system, highlighting the role of frustration and anisotropic interactions in stabilizing various magnetic phases.

Findings

Quantum phase transitions occur with increasing Kitaev interactions.

Frustrated exchange stabilizes stripe phases between Néel and Kitaev spin liquid.

Exact diagonalization reveals energy spectra and spin correlations.

Abstract

We present a detailed analysis of the Kitaev--Heisenberg model on a single hexagon. The energy spectra and spin--spin correlations obtained using exact diagonalisation indicate quantum phase transitions between antiferromagnetic and anisotropic spin correlations when the Kitaev interactions increase. In cluster mean-field approach frustrated nearest neighbor exchange stabilizes the stripe phase in between the N\'eel phase and frustrated one which evolves towards the Kitaev spin liquid.