Quantum Hall Fluids on the Haldane Sphere: A Diffusion Monte Carlo Study

A generalized diffusion Monte Carlo method for solving the many-body Schrödinger equation on curved manifolds is introduced and used to perform a “fixed-phase” simulation of the fractional quantum Hall effect on the Haldane sphere. This new method is used to study the effect of Landau level mixing on the $\nu =1\mathrm{}/3$ energy gap and the relative stability of spin-polarized and spin-reversed quasielectron excitations.