Knizhnik-Zamolodchikov equation and extended symmetry for stable Hall states

Details Knizhnik-Zamolodchikov equation and extended symmetry for stable Hall states Knizhnik-Zamolodchikov equation and extended symmetry for stable Hall states

1995-05-24

arxiv.org/abs/cond-mat/9505113v1

Physics

Condensed Matter

11 pages, Latex

Scientific paper

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.

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