Ordered states in the Kitaev-Heisenberg model: From 1D chains to 2D honeycomb

Cliò Efthimia Agrapidis,Jeroen Van Den Brink,Jeroen Van Den Brink,Satoshi Nishimoto,Satoshi Nishimoto

doi:10.1038/s41598-018-19960-4

Cliò Efthimia Agrapidis, Jeroen Van Den Brink + Show 3 more

Open Access

https://doi.org/10.1038/s41598-018-19960-4

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Abstract

We study the ground state of the 1D Kitaev-Heisenberg (KH) model using the density-matrix renormalization group and Lanczos exact diagonalization methods. We obtain a rich ground-state phase diagram as a function of the ratio between Heisenberg (J = cosϕ) and Kitaev (K = sinϕ) interactions. Depending on the ratio, the system exhibits four long-range ordered states: ferromagnetic-z, ferromagnetic-xy, staggered-xy, Néel-z, and two liquid states: Tomonaga-Luttinger liquid and spiral-xy. The two Kitaev points {boldsymbol{phi }}{boldsymbol{=}}frac{{boldsymbol{pi }}}{{bf{2}}} and {boldsymbol{varphi }}{boldsymbol{=}}frac{{bf{3}}{boldsymbol{pi }}}{{bf{2}}} are singular. The ϕ-dependent phase diagram is similar to that for the 2D honeycomb-lattice KH model. Remarkably, all the ordered states of the honeycomb-lattice KH model can be interpreted in terms of the coupled KH chains. We also discuss the magnetic structure of the K-intercalated RuCl3, a potential Kitaev material, in the framework of the 1D KH model. Furthermore, we demonstrate that the low-lying excitations of the 1D KH Hamiltonian can be explained within the combination of the known six-vertex model and spin-wave theory.

Highlights

We demonstrate that the low-lying excitations of the 1D KH Hamiltonian can be explained within the combination of the known six-vertex model and spin-wave theory
It is possible to establish a connection between our ground-state phase diagram and that of the two-dimensional KH model on a honeycomb lattice [Fig. 9(b), normalized to the current notation from10]
We have established the presence of a variety of phases in the 1D KH system

Summary

Introduction

All the ordered states of the honeycomb-lattice KH model can be interpreted in terms of the coupled KH chains. We obtain the ground-state phase diagram, including four long-range ordered and two liquid phases, as a function of the ratio between Heisenberg and Kitaev interactions. It is striking that all the magnetically ordered states of the honeycomb-lattice KH model can be interpreted in terms of coupled 1D KH chains.

Results

Conclusion