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arXiv · hep-th/0606286

On the NCCS model of the quantum Hall fluid

M. Eliashvili·G. Tsitsishvili
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Abstract

Area non-preserving transformations in the non-commutative plane are introduced with the aim to map the $ν=1$ integer quantum Hall effect (IQHE) state on the fractional quantum Hall effect (FQHE) $ν=\frac{1}{2p+1}$ FQHE states. Using the hydrodynamical description of the quantum Hall fluid, it is shown that these transformations are generated by vector fields satisfying the Gauss law in the interacting non-commutative Chern-Simons gauge theory, and the corresponding field-theory Lagrangian is reconstructed. It is demonstrated that the geometric transformations induce quantum-mechanical non-unitary similarity transformations, establishing the interplay between integral and fractional QHEs.

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M. Eliashvili, G. Tsitsishvili. 2007-03-21. On the NCCS model of the quantum Hall fluid. https://doi.org/10.1140/epjc%2Fs10052-007-0265-z

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