Interactions and non-commutativity in quantum Hall systems

doi:10.1088/0305-4470/38/45/008

Interactions and non-commutativity in quantum Hall systems

Author

Frederik G Scholtz ^1,2, Biswajit Chakraborty ^1,2, Sunandan Gangopadhyay ² and Jan Govaerts ³

Affiliations

¹ Institute of Theoretical Physics, University of Stellenbosch, Stellenbosch 7600, South Africa
² Satyendra Nath Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata - 700 098, India
³ Institute of Nuclear Physics, Department of Physics, Catholic University of Louvain 2, Chemin du Cyclotron, B-1348 Louvain-la-Neuve, Belgium

E-mail

fgs@sun.ac.za biswajit@bose.res.in sunandan@bose.res.in Jan.Govaerts@fynu.ucl.ac.be

Journal

Journal of Physics A: Mathematical and General Create an alert RSS this journal

Issue

Volume 38, Number 45

Citation

Frederik G Scholtz et al 2005 J. Phys. A: Math. Gen. 38 9849

doi: 10.1088/0305-4470/38/45/008

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Abstract

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. A 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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