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

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.

References in corpus (17)

• 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
• Fractional Chern Insulator
• Fractional Quantum Hall Physics in Topological Flat Bands
• The Insulating State of Matter: A Geometrical Theory
• Zoology of Fractional Chern Insulators
• Emergent Many-Body Translational Symmetries of Abelian and Non-Abelian Fractionally Filled Topological Insulators
• Adiabatic continuation of Fractional Chern Insulators to Fractional Quantum Hall States
• Disorder driven collapse of the mobility gap and transition to an insulator in fractional quantum Hall effect
• Non-Abelian Braiding of Lattice Bosons
• Fractional Chern insulator on a triangular lattice of strongly correlated $t_{2g}$ electrons
• Fractional Chern insulators with strong interactions far exceeding bandgaps
• Fractional quantum Hall states of few bosonic atoms in geometric gauge fields
• Exact diagonalization of the Hubbard model on graphics processing units
• Quantum phases of disordered flatband lattice fractional quantum Hall systems

Cited by in corpus (1)

• Exact diagonalization of quantum lattice models on coprocessors