Toward the construction of a realistic Hamiltonian for the bosonic Moore-Read Pfaffian state at ν=1

Over the course of several decades physical systems that support topologically ordered phases have garnered interest due to the possibility of fractional braiding statistics among the low energy quasiparticle excitations, which hold promising practical applications. The fermionic case of the fractional quantum Hall effect at filling factor 5/2, thought to support these non-Abelian excitations, is experimentally challenging. Alternatively, the setting which can engender bosonic fractional quantum Hall states in different realistic physical systems has been established. Using exact diagonalization, we study the low-energy spectrum of a two-body model Hamiltonian generated from the three-body Hamiltonian that produces the Pfaffian as its zero-energy ground state for bosons in the spherical geometry (similar to the method used by Peterson, et al (Phys. Rev. Lett. 101, 156803 (2008)). Moreover, we analyze whether this realistic(two-body) Hamiltonian supports robust non-Abelian excitations.