Ground state and low-energy excitations of the Kitaev-Heisenberg two-leg ladder

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=sinϕ and J=cosϕ with an angle parameter ϕ. Based on the results for several types of order parameters, excitation gaps, string order parameter, and entanglement spectra, the ϕ-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 ϕ=±π/2. We also calculate the expectation value of a plaquette operator corresponding to a π-flux state in order to establish how the gapped Kitaev spin liquid extends away from the ϕ=±π/2. Furthermore, we determine the dynamical spin structure factor and discuss the effect of the Kitaev interaction on the spin-triplet dispersion.