Interactions and non-commutativity in quantum Hall systems

Details Interactions and non-commutativity in quantum Hall systems Interactions and non-commutativity in quantum Hall systems

2005-09-13

arxiv.org/abs/cond-mat/0509331v1

J.Phys.A38:9849-9858,2005

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

8 pages, 2 figures

Scientific paper

10.1088/0305-4470/38/45/008

We discuss the role that interactions play in the non-commutative structure that arises when the relative coordinates of two interacting particles are projected onto the lowest Landau level. It is shown that the interactions in general renormalize the non-commutative parameter away from the non-interacting value $\frac{1}{B}$. The effective non-commutative parameter is in general also angular momentum dependent. An heuristic argument, based on the non-commutative coordinates, is given to find the filling fractions at incompressibilty, which are in general renormalized by the interactions, and the results are consistent with known results in the case of singular magnetic fields.

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