We study the ground state and low-lying excited states of the Kitaev-Heisenberg model on a two-leg ladder geometry using the density-matrix renormalization-group and Lanczos exact diagonalization methods. The Kitaev and Heisenberg interactions are parametrized as $K=sin\varphi$ and $J=cos\varphi$ with an angle parameter $\varphi$. Based on the results for several types of order parameters, excitation gaps, string order parameter, and entanglement spectra, the $\varphi$-dependent ground state phase diagram is determined. Remarkably, the phase diagram is quite similar to that of the Kitaev-Heisenberg model on a honeycomb lattice, exhibiting the same long-range-ordered states, namely rung singlet (analog to Néel in three dimensions), zigzag, ferromagnetic, and stripy, and the presence of gapped spin liquids around the exactly solvable Kitaev points $\varphi =\pm \pi /2$. We also calculate the expectation value of a plaquette operator corresponding to a $\pi$-flux state in order to establish how the gapped Kitaev spin liquid extends away from the $\varphi =\pm \pi /2$. Furthermore, we determine the dynamical spin structure factor and discuss the effect of the Kitaev interaction on the spin-triplet dispersion.

• Received 11 February 2019
• Revised 27 May 2019

DOI:https://doi.org/10.1103/PhysRevB.99.224418