Model anisotropic quantum Hall states

TL;DR

This paper generalizes key quantum Hall states into anisotropic forms, showing they are exact eigenstates of specific Hamiltonians and can describe systems with anisotropic interactions, supported by numerical results.

Contribution

It introduces anisotropic versions of Laughlin, Moore-Read, and Read-Rezayi states as exact eigenstates, highlighting geometric degrees of freedom in fractional quantum Hall systems.

Findings

Anisotropic quantum Hall states are exact zero-energy eigenstates.

Generalized states effectively describe systems with anisotropic interactions.

Numerical results support the validity of the anisotropic models.

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 multi-body Hamiltonians, and explicitly illustrate the existence of geometric degrees of 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.