Ground-state phase diagram of the Kitaev-Γ model on a honeycomb lattice

We investigate the ground-state phase diagram of the Kitaev-Γ model on a honeycomb lattice by utilizing several numerical methods, such as the numerical exact-diagonalization method and the density-matrix-renormalization-group method. In this study, we focus on the effect of the anisotropic interaction; we connect the isolated dimer limit and the spin-chain limit by changing the coupling constants. From the numerical results, we find that there are three kinds of phases, namely the Tomonaga-Luttinger (TL) liquid phase and two kinds of magnetic ordered states, in the spin-chain limit. When the Γ interaction is positive and the Kitaev interaction is negative, the TL liquid is stable against the interchain couplings, which implies that the TL liquid survives up to the vicinity of the isotropic point or shows a crossover behavior. The dimer phases also survive in the vicinity of the isotopic limit. We expect that many states are competing around the isotropic point.