  The properties of fractional Chern insulator (FCI) phase and the phase
transitions between FCI and Mott insulators (MI) in bosonic systems are well
studied. The continuous transitions between FCI and superfluid (SF), however,
despite the inspiring field theoretical predictions, have not been directly
verified. The existing numerical results of FCI-SF transition are either
indirect or clearly first-order. Here, by simply tuning the bandwidth of
Haldane honeycomb lattice model, we find direct transitions from a bosonic FCI
at $\nu$ = 1/2 filling of a flat Chern band to two SF states with bosons
condensed at momenta $M$ and $\Gamma$, respectively. While the FCI-SF($M$)
transition is first-order, the FCI-SF($\Gamma$) transition is found continuous.
Through finite size criticality analysis, the obtained critical exponents
$\beta\approx$0.35(5) and $\nu\approx$0.62(12) are both compatible with those
of the 3D XY universality class and more exotic beyond-Landau ones. Our work
thence presents a direct numerical evidence of a continuous FCI-SF transition
between topological ordered phase and spontaneous continuous symmetry-breaking
phase, and further indicates the zero-field bosonic FCI might be realized from
a SF state by gradually flattening the dispersion of Chern band, through the
(quasi)adiabatic preparation in ultracold atom systems.
