  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.
