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arXiv · hep-th/0103179

Quantum Hall Physics = Noncommutative Field Theory

Simeon Hellerman·Mark Van Raamsdonk
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Abstract

In this note, we study a matrix-regularized version of non-commutative U(1) Chern-Simons theory proposed recently by Polychronakos. We determine a complete minimal basis of exact wavefunctions for the theory at arbitrary level k and rank N and show that these are in one-to-one correspondence with Laughlin-type wavefunctions describing excitations of a quantum Hall droplet composed of N electrons at filling fraction 1/k. The finite matrix Chern-Simons theory is shown to be precisely equivalent to the theory of composite fermions in the lowest Landau level, believed to provide an accurate description of the filling fraction 1/k fractional quantum Hall state. In the large N limit, this implies that level k noncommutative U(1) Chern-Simons theory is equivalent to the Laughlin theory of the filling fraction 1/k quantum Hall fluid, as conjectured recently by Susskind.

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Simeon Hellerman, Mark Van Raamsdonk. 2001-08-16. Quantum Hall Physics = Noncommutative Field Theory. https://doi.org/10.1088/1126-6708%2F2001%2F10%2F039

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