Impurities and Landau level mixing in a fractional quantum Hall state in a flatband lattice model

TL;DR

This study investigates the stability of a fractional quantum Hall state in a lattice model under impurities and Landau level mixing, revealing phase transitions and the robustness of the lowest Landau level approximation.

Contribution

It provides a detailed numerical analysis of impurity effects and Landau level mixing on fractional quantum Hall states in a lattice model without Landau level projection.

Findings

Phase transitions from fractional quantum Hall to metallic and insulating phases due to impurities.

Impurity hoppings induce a transition to insulators at high densities.

Landau level mixing remains weak even with strong interactions and impurities.

Abstract

We study the toplogical checkerboard lattice model around the $\nu=\frac{1}{3}$ fractional quantum Hall phase using numerical exact diagonalization without Landau level projections. We add local perturbations, modified hoppings and on-site potentials, and observe phase transitions from the fractional quantum Hall phase to metallic and insulating phases when the strength and number of impurities is increased. In addition to evaluating the energy spectrum, we identify the phase diagrams by computing the topological Chern number of the many-body ground state manifold, and we show how the ground states lose their correlations due to the impurities by evaluating the spectrum of the one-body reduced density matrix. Our results show that the phase transition from the fractional quantum Hall phase to the metallic phase occurs for both impurity hoppings and potentials. Strong impurity hoppings cause a further transition into the insulating state, regardless of the sign of the hopping, when their density is high enough. In contrast, the same happens only for attractive potentials. Furthermore, the mixing to the higher band in a two-band model, generally denoted as Landau level mixing, is measured concluding that the lowest Landau level projection works well even with remarkably strong interactions and in the presence of impurities.