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

A striking feature of fractional quantum Hall states is that they form an incompressible quantum state
supporting emergent fractionally charged quasiparticle excitations with non trivial braiding properties.
Excitations of non-Abelian nature command much attention from theorists and experimentalists due to
their potential applications in quantum information especially topologically protected fault tolerant quantum computation.
This talk will present Ising quasiholes in Moore-Read type lattice wave functions. We start by 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.