Quantum Hall Physics = Noncommutative Field Theory
Quantum Hall Physics = Noncommutative Field Theory
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DOI：
10.1088/1126-6708/2001/10/039
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发表时间：
2001-03
期刊：
影响因子：
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通讯作者：
S. Hellerman;M. Raamsdonk
中科院分区：
文献类型：
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作者：
S. Hellerman;M. Raamsdonk
本文研究了Polychronakos最近提出的非对易U（1）Chern-Simons理论的矩阵正则化形式.我们确定了一个完整的最小基础的理论在任意级别k和秩N的精确波函数，并表明这些是在一对一的对应关系与Laughlin型波函数描述的激发的量子霍尔液滴组成的N电子在填充分数1/k。有限矩阵Chern-Simons理论与复合费米子理论在最低朗道能级上是完全等价的，可以精确描述填充分数为1/k的分数量子Hall态.在大N极限下，这意味着k阶非对易U（1）Chern-Simons理论等价于Susskind最近提出的填充分数为1/k的量子Hall流体的Laughlin理论.
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.