Quantum Hall hierarchy in a spherical geometry

摘要: Representative wave functions, which encode the topological properties of spin polarized fractional quantum Hall states in lowest Landau level, can be expressed terms correlation functions conformal field theories. Until now, constructions have been restricted to flat geometries, but this paper we generalize simplest curved geometry, namely that a sphere. Except for being interest numerical studies, usually are performed on sphere, response (FQH) liquids curvature used detect quantity, shift S is average orbital constituent electrons. We give explicit expressions representative full Abelian FQH hierarchy, and calculate corresponding shifts. These microscopic results, based agree with predictions from effective Chern-Simons theory. The methods develop also applied planar case. It gives simpler both quasiparticle quasihole condensates, allows us closed form general state rather than finding function case by basis.