We estimate phase boundaries of four ordered and two spin-liquid phases for the spin-$\frac{ 1}{ 2}$ Kitaev-Heisenberg (KH) model using four kinds of relatively-small clusters, based on the second derivative of ground-state energy. The estimated values are compared between the clusters as well as the previous iPEPS results. We thus find that the boundaries can be accurately estimated within limited-size clusters. The used clusters may appropriate to study higher-$S$ KH models having less fluctuations.
Categories: cond-mat.str-el