Quasielectrons as inverse quasiholes in lattice fractional quantum Hall models

Abstract

From an experimental point of view, quasielectrons and quasiholes play very similar roles in the fractional quantum Hall effect. Nevertheless, the theoretical description of quasielectrons is known to be much harder than the one of quasiholes. The problem is that one obtains a singularity in the wavefunction if one tries to naively construct the quasielectron as the inverse of the quasihole. Here, we demonstrate that the same problem does not arise in lattice fractional quantum Hall models. This result allows us to make detailed investigations of the properties of quasielectrons, including their braiding statistics and density distribution on lattices on the plane and on the torus. We show that some of the states considered have high overlap with certain fractional Chern insulator states. We also derive few-body Hamiltonians, for which various states containing quasielectrons are exact ground states.

13 pages, 4 figures, v3: accepted version

References in corpus (12)

• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Fractional Quantum Hall Effect in Optical Lattices
• Non-Abelian Statistics in a Quantum Antiferromagnet
• Clustering Properties and Model Wavefunctions for Non-Abelian Fractional Quantum Hall Quasielectrons
• Braiding non-Abelian quasiholes in fractional quantum Hall states
• Emergence of fractional statistics for tracer particles in a Laughlin liquid
• Fractional angular momentum in cold atom systems
• Berry phases for composite fermions: effective magnetic field and fractional statistics
• Anyon braiding in semi-analytical fractional quantum Hall lattice models
• Characterization of quasiholes in fractional Chern insulators
• Lattice effects on Laughlin wave functions and parent Hamiltonians

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• Charge and statistics of lattice quasiholes from density measurements: a Tree Tensor Network study
• Measurable signatures of bosonic fractional Chern insulator states and their fractional excitations in a quantum-gas microscope
• Optical control over bulk excitations in fractional quantum Hall systems
• Quasiparticles as Detector of Topological Quantum Phase Transitions
• Model wavefunctions for interfaces between lattice Laughlin states
• Squeezing anyons for braiding on small lattices
• Quasielectrons in lattice Moore-Read models
• Characterization of fractional Chern insulator quasiparticles in twisted homobilayer MoTe${}_2$
• Mechanism for particle fractionalization and universal edge physics in quantum Hall fluids
• Anyonic quasiparticles of hardcore anyons
• Properties of Laughlin states on fractal lattices
• Continuum limit of lattice quasielectron wavefunctions
• Dynamics of quasiholes and quasiparticles at the edges of small lattices