Particle-Hole Symmetry Breaking in the Fractional Quantum Hall Effect at ν = 5/2

The fractional quantum Hall effect (FQHE) in the half-filled second Landau level (filling factor ν = 5/2) offers new insights into the physics of exotic emergent quasi-particles. The FQHE is due to the collective interactions of electrons confined to two-dimensions, cooled to sub-Kelvin temperatures, and subjected to a strong perpendicular magnetic field. Under these conditions a quantum liquid forms displaying quantized plateaus in the Hall resistance and chiral edge flow. The leading candidate description for the FQHE at 5/2 is provided by the Moore-Read Pfaffian state which supports non-Abelian anyonic low-energy excitations with potential applications in fault-tolerant quantum computation schemes. The Moore-Read Pfaffian is the exact zero-energy ground state of a particular three-body Hamiltonian and explicitly breaks particle-hole symmetry. In this thesis we investigate the role of two and three body interaction terms in the Hamiltonian and the role of particle hole symmetry (PHS) breaking at ν = 5/2. We start with a PHS two body Hamiltonian (H 2) that produces an exact ground state that is nearly identical with the Moore-Read Pfaffian and construct a Hamiltonian H(α) = (1 – α)H3 + α H 2 that tunes continuously between H3 and H2. We find that the ground states, and low-energy excitations, of H2 and H3 are in one-to-one correspondence and remain adiabatically connected indicating they are part of the same universality class and describe the same physics in the thermodynamic limit. In addition, evidently three body PHS breaking interactions are not a crucial ingredient to realize the FQHE at 5/2 and the non-Abelian quasiparticle excitations