Hierarchical Wave Functions of Fractional Quantum Hall Effect on the Torus

TL;DR

This paper constructs hierarchical wave functions for the fractional quantum Hall effect on a torus, revealing their close relation to generalized Abelian Chern-Simons theory, advancing understanding of topological quantum states.

Contribution

It introduces a new class of hierarchical wave functions on the torus and links them to Chern-Simons theory, providing a novel theoretical framework.

Findings

Hierarchical wave functions are explicitly constructed.

Wave functions are shown to relate to Abelian Chern-Simons theory.

The work enhances understanding of topological order in quantum Hall systems.

Abstract

One kind of the hierarchical wave functions of Fractional Quantum Hall Effect on the torus is constructed. We find that the wave functions closely relate to the wave functions of generalized Abelian Chern-Simons theory.