Quantum phases of disordered flatband lattice fractional quantum Hall systems

TL;DR

This study maps out the quantum phase diagram of disordered lattice fractional quantum Hall systems, revealing transitions from FQH states to trivial insulators driven by disorder and interactions.

Contribution

It introduces a detailed numerical analysis of disorder effects on lattice FQH systems, identifying phase transitions and characterizing phases using multiple quantum metrics.

Findings

FQH state transitions to a trivial insulator with increasing disorder

Energy gap and Chern number calculations confirm phase boundaries

Disorder induces a sequence of quantum phase transitions

Abstract

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.