Numerical Study of the Kitaev-Heisenberg chain as a spin model of the K-intercalated RuCl3

We study the one-dimensional Kitaev-Heisenberg model as a possible realization of magnetic degrees of freedom of the K-intercalated honeycomb-lattice ruthenium trichloride α-RuCl3, denoted as K0.5RuClm. First, we discuss the possible charge ordering patterns in K0.5RuClm, where half of the j=12 spins are replaced by nonmagnetic ions in the honeycomb layer. The phase diagram is obtained as a function of nearest-, second-, and third-neighbor repulsions in the atomic limit. We find a strong competition between possible three charge ordering patterns when the repulsions are comparable. We further calculate the spin-spin correlation functions for the 1D Kitaev-Heisenberg model, which is one of the ordering patterns, and consider the effect of the Kitaev term by comparing the results to those for the antiferromagnetic SU(2) Heisenberg chain.