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 = sin phi and J = cos phi with an angle parameter phi. Based on the results for several types of order parameters, excitation gaps, string order parameter, and entanglement spectra, the phi-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 Neel in three dimensions), zigzag, ferromagnetic, and stripy, and the presence of gapped spin liquids around the exactly solvable Kitaev points phi = +/-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 phi = +/-pi/2. Furthermore, we determine the dynamical spin structure factor and discuss the effect of the Kitaev interaction on the spin-triplet dispersion.