Evolution of the optimal trial wave function of fractional Chern insulators with interactions

We demonstrate the evolution of the optimal trial wave function of fractional Chern insulators(FCI) with interactions in checkerboard model. The gauge of the single particle Bloch states for constructing the optimal wave function is obtained by applying the interaction energy variational principle proposed by Zhang et al.. We consider the short-range interaction, coulomb interaction, and an interpolation between them. We find that the optimal gauge critically depends on the forms of interaction. In particular, we compare the optimal gauge with those proposed by Qi and Wu et al., and find that Wu et al.'s gauge can be close to the optimal gauge when interaction is close to coulomb interaction, while Qi's gauge is qualitatively different from the optimal gauge in all the cases.