Non-Abelian quasiholes in lattice Moore-Read states and parent Hamiltonians

TL;DR

This paper constructs and analyzes lattice Moore-Read states with non-Abelian quasiholes, demonstrating their topological braiding properties and deriving parent Hamiltonians that allow quasihole braiding through Hamiltonian parameter adjustments.

Contribution

It introduces a method to construct Moore-Read lattice states with quasiholes, analyzes their properties, and derives parent Hamiltonians enabling quasihole braiding by tuning couplings.

Findings

Quasiholes exhibit continuum-like braiding properties.

Parent Hamiltonians are derived for quasihole states.

Hamiltonian tuning allows quasihole braiding.

Abstract

This work concerns Ising quasiholes in Moore-Read type lattice wave functions derived from conformal field theory. We commence with constructing Moore-Read type lattice states and then add quasiholes to them. By use of Metropolis Monte Carlo simulations, we analyze the features of the quasiholes, such as their size, shape, charge, and braiding properties. The braiding properties, which turn out to be the same as in the continuum Moore-Read state, demonstrate the topological attributes of the Moore-Read lattice states in a direct way. We also derive parent Hamiltonians for which the states with quasiholes included are ground states. One advantage of these Hamiltonians lies therein that we can now braid the quasiholes just by changing the coupling strengths in the Hamiltonian since the Hamiltonian is a function of the positions of the quasiholes. The methodology exploited in this article can also be used to construct other kinds of lattice fractional quantum Hall models containing quasiholes, for example investigation of Fibonacci quasiholes in lattice Read-Rezayi states.