Quasielectrons in lattice Moore-Read models

TL;DR

This paper demonstrates that lattice Moore-Read states can host both quasiholes and quasielectrons without singularities, enabling detailed analysis of anyon properties and providing an exact parent Hamiltonian.

Contribution

It introduces a method to construct Moore-Read Pfaffian states with quasielectrons on lattices, overcoming previous singularity issues in continuous systems.

Findings

Successful construction of lattice Moore-Read states with quasielectrons

Monte Carlo simulations reveal density, charge, and braiding properties of anyons

Derived an exact few-body parent Hamiltonian for these states

Abstract

Moore-Read states can be expressed as conformal blocks of the underlying rational conformal field theory, which provides a well explored description for the insertion of quasiholes. It is known, however, that quasielectrons are more difficult to describe in continuous systems, since the natural guess for how to construct them leads to a singularity. In this work, we show that the singularity problem does not arise for lattice Moore-Read states. This allows us to construct Moore-Read Pfaffian states on lattices for filling fraction 5/2 with both quasiholes and quasielectrons in a simple way. We investigate the density profile, charge, size and braiding properties of the anyons by means of Monte Carlo simulations. Further we derive an exact few-body parent Hamiltonian for the states. Finally, we compare our results to the density profile, charge and shape of anyons in the Kapit-Mueller model by means of exact diagonalization.