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

We show that the optimal trial wave function of a fractional Chern insulator depends on the form of its electron-electron interaction. The gauge of single particle Bloch bases for constructing the optimal trail wave function is obtained by applying the variational principle proposed by Zhang et al. [Phys. Rev. B 93, 165129 (2016)]. We consider a short-range interaction, the Coulomb interaction, and an interpolation between them, and determine the evolution of the optimal gauge with the different interactions. We compare the optimal gauge with those proposed by Qi [Phys. Rev. Lett. 107, 126803 (2011)] and Wu et al. [Phys. Rev. B 86, 085129 (2012)], and find that Wu et al.'s gauge is close to the optimal gauge when the interaction is a certain mixture of the Coulomb interaction and the short-range interaction, while Qi's gauge is qualitatively different from the optimal gauge in all the cases. Both the gauges deviate significantly from the optimal gauge when the short-range component of the interaction becomes more prominent.