Laughlin states on the Poincare half-plane and its quantum group symmetry

TL;DR

This paper explores Laughlin states of electrons on the Poincare half-plane, revealing a quantum group symmetry and calculating the filling factor using plasma analogy, advancing understanding of fractional quantum Hall effects in curved spaces.

Contribution

It demonstrates that Laughlin states on the Poincare half-plane form representations of the quantum group $su_q(2)$, linking geometric and algebraic structures in quantum Hall systems.

Findings

Existence of quantum group $su_q(2)$ symmetry for Laughlin states

Calculation of filling factor via plasma analogy

Representation of Laughlin states in different geometric representations

Abstract

We find the Laughlin states of the electrons on the Poincare half-plane in different representations. In each case we show that there exist a quantum group $su_q(2)$ symmetry such that the Laughlin states are a representation of it. We calculate the corresponding filling factor by using the plasma analogy of the FQHE.