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

The essence of the nu = 5/2 fractional quantum Hall effect is believed to be captured by the Moore-Read Pfaffian (or anti-Pfaffian) description. However, a mystery regarding the formation of the Pfaffian state is the role of the three-body interaction Hamiltonian H-3 that produces it as an exact ground state and the concomitant particle-hole symmetry breaking. We show that a two-body interaction Hamiltonian H-2 constructed via particle-hole symmetrization of H-3 produces a ground state nearly exactly approximating the Pfaffian and anti-Pfaffian states, respectively, in the spherical geometry. Importantly, the ground state energy of H-2 exhibits a Mexican-hat structure as a function of particle number in the vicinity of half filling for a given flux indicating spontaneous particle-hole symmetry breaking. This signature is absent for the second Landau level Coulomb interaction at 5/2.