Quasielectrons as inverse quasiholes in lattice fractional quantum Hall models

TL;DR

This paper explores the properties of quasielectrons in lattice fractional quantum Hall models, revealing that they can be treated as inverse quasiholes without singularities, enabling detailed analysis of their braiding and density characteristics.

Contribution

It demonstrates that quasielectrons can be modeled as inverse quasiholes in lattice FQH systems, overcoming previous theoretical difficulties and enabling new investigations.

Findings

Quasielectrons can be treated as inverse quasiholes without singularities.

Some states have high overlap with fractional Chern insulator states.

Derived few-body Hamiltonians with quasielectron states as exact ground states.

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.