  We study an extended Kitaev-Heisenberg model including additional anisotropic
couplings by using two-dimensional density-matrix renormalization group method.
Calculating the gound-state energy, entanglement entropy, and spin-spin
correlation functions, we make a phase diagram of the extended
Kitaev-Heisenberg model around spin-liquid phase. We find a zigzag
antiferromagnetic phase, a ferromagnetic phase, a 120-degree antiferromagnetic
phase, and two kinds of incommensurate phases around the Kitaev spin-liquid
phase. Furthermore, we study the entanglement spectrum of the model and find
that entanglement levels in the Kitaev spin-liquid phase are degenerate forming
pairs but those in the magnetically ordered phases are non-degenerate. The
Schmidt gap defined as the energy difference between the lowest two levels
changes at the phase boundary adjacent to the Kitaev spin-liquid phase.
However, we find that phase boundaries between magnetically ordered phases do
not necessarily agree with the change of the Schmidt gap.

Strongly Correlated Electrons