Applications of Quantum Group to FQH Effect

TL;DR

This paper explores how quantum group symmetry, specifically $sl_q(2)$, influences the degeneracy of ground states in the fractional quantum Hall effect, including effects of impurities and boundary conditions.

Contribution

It demonstrates the presence of quantum group symmetry in FQHE and links ground state degeneracy to cyclic representations of $SL_q(2)$ under periodic boundary conditions.

Findings

Quantum group symmetry $sl_q(2)$ exists in FQHE.

Ground state degeneracy relates to cyclic representations of $SL_q(2)$.

Impurities affect the ground state properties.

Abstract

We show that there exists quantum group symmetry $ sl_{q}(2) $ in the fractional quantum Hall effect (FQHE) and this symmetry governs the degeneracy of ground-state level. Under the periodic boundary condition, the degeneracy of the ground state is related to the cyclic representation of SL_q(2). We also discuss the influence of impurity.