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Finite matrix model of quantum hall fluids on S2

Published online by Cambridge University Press:  17 April 2009

Yi-Xin Chen ,
Mark D. Gould  and
Yao-Zhong Zhang
Yi-Xin Chen
Affiliation:
Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027, Peoples Republic of China and Department of Mathematics, The University of Queensland, Queensland 4072, Australia, e-mail: yxchen@zimp.zju.edu.cn
Mark D. Gould
Affiliation:
Department of Mathematics, The University of Queensland, Queensland 4072, Australia
Yao-Zhong Zhang
Affiliation:
Department of Mathematics, The University of Queensland, Queensland 4072, Australia e-mail: yzz@maths.uq.edu.au
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Based on Haldane's spherical geometrical formalism of the two-dimensional quantum Hall fluids, the relation between the noncommutative geometry of S2 and the two-dimensional quantum Hall fluids is exhibited. A finite matrix model on the two-sphere is explicitly constucted as an effective description of the fractional quantum Hall fluids of finite extent, and the complete sets of physical quantum states of this matrix model are determined. We also describe how the low-lying excitations in the model are constructed in terms of the quasi-particle and quasi-hole excitations. It is shown that there exists a Haldane hierarchical structure in the two-dimensional quantum Hall fluid states of the matrix model. These hierarchical fluid states are generated by the parent fluid state by condensing the quasi-particle and quasi-hole excitations level by level.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 76 , Issue 1 , August 2007 , pp. 111 - 132
Copyright
Copyright © Australian Mathematical Society 2007

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