Origin of the ν= 1/2 fractional quantum Hall effect in wide quantum wells

Previous studies have investigated the nature of the fractional quantum Hall effect at $\nu=1/2$ observed in wide quantum wells by the variational Monte Carlo method, which makes the assumption that the transverse wave function and the gap between the symmetric and antisymmetric subbands obtained in a local density approximation at zero magnetic field remain valid even at high perpendicular magnetic fields; this method also ignores the effect of Landau level mixing. We develop a three-dimensional fixed phase diffusion Monte Carlo(DMC) method, which gives, in a single framework, the total energies of various candidate states in a finite width quantum well, including Landau level mixing, directly in a large magnetic field. This method can be applied to one-component states, as well two-component states in the limit where the symmetric and antisymmetric bands are nearly degenerate. Our three-dimensional fixed-phase DMC calculations suggest that the observed 1/2 fractional quantum Hall state in wide quantum wells is likely to be the one-component Pfaffian state supporting non-Abelian excitations. We also study the influence of the asymmetry of the quantum well on the ground states.