Quantum phases of disordered flatband lattice fractional quantum Hall systems

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.

5 pages, 4 figures

References in corpus (6)

• Non-Abelian Anyons and Topological Quantum Computation
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Fractional quantum Hall effect in the absence of Landau levels
• Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model

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• Momentum-space instantons and maximally localized flat-band topological Hamiltonians
• Thermal crossover from a Chern insulator to a fractional Chern insulator in pentalayer graphene
• Integer and fractional quantum anomalous Hall effects in pentalayer graphene
• Single and double linear and nonlinear flatband chains: spectra and modes
• Intertwining SU($N$) symmetry and frustration on a honeycomb lattice
• Fractional quantum anomalous Hall effect in rhombohedral multilayer graphene with a strong displacement field
• On the zero-field quantization of the anomalous quantum Hall effect in moiré 2D layers
• Impurities and Landau level mixing in a fractional quantum Hall state in a flatband lattice model
• Quantum Fidelity of the Aubry-André Model and the Exponential Orthogonality Catastrophe