Title: Ordered states in the Kitaev-Heisenberg model: From 1D chains to 2D honeycomb,
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 ($J=\cos\phi)$ and Kitaev ($K=\sin\phi$) 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
$\phi=\frac{\pi}{2}$ and $\phi=\frac{3\pi}{2}$ are singular. The
$\phi$-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 RuCl$_3$, 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.