Study of Kitaev-Heisenberg model with second-neighbor Heisenberg coupling by DMRG simulations and slave-particle theories

We study the effect of second-neighbor Heisenberg coupling $J_2$ to the first neighbor Kitaev-Heisenberg model on the honeycomb lattice by doing DMRG simulations and slave-particle theories. In the Kitaev limit, we find that the gapless spin liquid phase at $J_2=0$ survives up to a finite critical value $J_{2c}$. In an intermediate range, namely $J_{2c}