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.

arXiv comment5 pages, 4 figures

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• Moiré Fractional Chern Insulators III: Hartree-Fock Phase Diagram, Magic Angle Regime for Chern Insulator States, the Role of the Moiré Potential and Goldstone Gaps in Rhombohedral Graphene Superlattices
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• 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
• Exact diagonalization of quantum lattice models on coprocessors
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• Quantum Fidelity of the Aubry-André Model and the Exponential Orthogonality Catastrophe