Knizhnik-Zamolodchikov equation and extended symmetry for stable Hall states

TL;DR

This paper models multi-component abelian Hall fluids using composite bosons and links their collective states to Knizhnik-Zamolodchikov equations, revealing an extended symmetry algebra relevant for understanding edge states.

Contribution

It introduces a novel description of multi-component Hall states via KZ equations and uncovers an extended symmetry algebra for Jain's sequences.

Findings

KZ equations characterize the collective vacuum state.

Extended $alU(1) alSU(n)$ algebra emerges for Jain states.

Only the $alU(1)$ mode carries charge, $alSU(n)$ modes are neutral.

Abstract

We describe a $n$ component abelian Hall fluid as a system of {\it composite bosons} moving in an average null field given by the external magnetic field and by the statistical flux tubes located at the position of the particles. The collective vacuum state, in which the bosons condense, is characterized by a Knizhnik-Zamolodchikov differential equation relative to a $\hat {U}(1)^n$ Wess-Zumino model. In the case of states belonging to Jain's sequences the Knizhnik-Zamolodchikov equation naturally leads to the presence of an $\hat{U}(1)\ot \hat{SU}(n)$ extended algebra. Only the $\hat{U}(1)$ mode is charged while the $\hat{SU}(n)$ modes are neutral, in agreement with recent results obtained in the study of the edge states.