Quantum phases of disordered flatband lattice fractional quantum Hall systems

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 the numerically calculated energy gap, quantum degeneracy, the Chern number, the entanglement spectrum, and the fidelity metric to identify various quantum phases. The connection to continuum FQH effects is also discussed.