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We study an extended Kitaev-Heisenberg model including additional anisotropiccouplings by using two-dimensional density-matrix renormalization group method.Calculating the gound-state energy, entanglement entropy, and spin-spincorrelation functions, we make a phase diagram of the extendedKitaev-Heisenberg model around spin-liquid phase. We find a zigzagantiferromagnetic phase, a ferromagnetic phase, a 120-degree antiferromagneticphase, and two kinds of incommensurate phases around the Kitaev spin-liquidphase. Furthermore, we study the entanglement spectrum of the model and findthat entanglement levels in the Kitaev spin-liquid phase are degenerate formingpairs but those in the magnetically ordered phases are non-degenerate. TheSchmidt gap defined as the energy difference between the lowest two levelschanges at the phase boundary adjacent to the Kitaev spin-liquid phase.However, we find that phase boundaries between magnetically ordered phases donot necessarily agree with the change of the Schmidt gap.

Density-Matrix Renormalization Group Study of Extended Kitaev-Heisenberg Model