  By numerical exact diagonalization techniques, we obtain the quantum phase
diagram of the lattice fractional quantum Hall (FQH) systems in the presence of
quenched disorder. By implementing an array of local potential traps
representing the disorder, we show that the system undergoes a series of
quantum phase transitions as the disorder and/or the interaction is tuned. As
the strength of potential traps is increased, the FQH state turns into a
compressible liquid, and then into a topologically trivial insulator. We use
numerically calculated energy gap, quantum degeneracy, Chern number,
entanglement spectrum, and fidelity to identify various quantum phases. The
connection to continuum FQH effects is also discussed.
