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

Abstract

We study the ground state and low-lying excited states of the Kitaev-Heisenberg model on a 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, 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 3D), zigzag, ferromagnetic, and stripy; and the presence of Kitaev 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 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.

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