  Topological nontrivial bands can be realized via Rydberg-dressed neutral
atoms. We propose a two-dimensional hard-core boson model with a topological
ground enrgy at band on a honeycomb lattice, where the particle hopping is
realized via van der Waals interaction that exchanges the Rydberg states of two
interacting atoms, while nonzero phases associated with hopping is created by
transferring the optical phase of laser fields to the atomic pair wave
function. Using exactly diagonalization and infinite density matrix
renormalization group simulation, we find in the system a fractional Chern
insulator phase with a Chern number C = 1/2, which can persist in the presence
of weak many-body interactions. Our studies indicate that fractional Chern
insulators can be studied with neutral-atom arrays.
