Model anisotropic quantum Hall states

Abstract

Model quantum Hall states including Laughlin, Moore-Read, and Read-Rezayi states are generalized into appropriate anisotropic form. The generalized states are exact zero-energy eigenstates of corresponding anisotropic two- or multibody Hamiltonians, and explicitly illustrate the existence of geometric degree of freedom in the fractional quantum Hall effect. These generalized model quantum Hall states can provide a good description of the quantum Hall system with anisotropic interactions. Some numeric results of these anisotropic quantum Hall states are also presented.