Disordered Interactions and Fractional Quantum Hall States

Ivan V. Protopopov, Yuval Gefen, A. D. Mirlin

S. B. Mulay, John J. Quinn, Mark Shattuck

Zhao Liu, R. N. Bhatt

Min Lu, Na Jiang, Xin Wan

Fractional quantum Hall systems are often described by model wave functions, which are the ground states of pure systems with short-range interaction. A primary example is the Laughlin wave function, which supports Abelian quasiparticles with fractionalized charge. In the presence of disorder, the wave function of the ground state is expected to deviate from the Laughlin form. We study the disorder-driven collapse of the quantum Hall state by analyzing the evolution of the ground state and the single-quasihole state. In particular, we demonstrate that the quasihole tunneling amplitude can signal the fractional quantum Hall phase to insulator transition.

Nicolas Regnault

Shuo Yang, Kai Sun, S. Das Sarma

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.