Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-08-06
Physics
High Energy Physics
High Energy Physics - Theory
LaTex file, 19 pages
Scientific paper
Based on Haldane's spherical geometrical formalism of two-dimensional quantum Hall fluids, the relation between the noncommutative geometry of $S^2$ and the two-dimensional quantum Hall fluids is exhibited. If the number of particles $N$ is infinitely large, two-dimensional quantum Hall physics can be precisely described in terms of the noncommutative U(1) Chern-Simons theory proposed by Susskind, like in the case of plane. However, for the finite number of particles on two-sphere, the matrix-regularized version of noncommutative U(1) Chern-Simons theory involves in spinor oscillators. We establish explicitly such a finite matrix model on two-sphere as an effective description of fractional quantum Hall fluids of finite extent. The complete sets of physical quantum states of this matrix model are determined, and the properties of quantum Hall fluids related to them are discussed. We also describe how the low-lying excitations are constructed in terms of quasiparticle and quasihole excitations in the matrix model. It is shown that there consistently exists a Haldane's hierarchical structure of two-dimensional quantum Hall fluid states in the matrix model. These hierarchical fluid states are generated by the parent fluid state for particles by condensing the quasiparticle and quasihole excitations level by level, without any requirement of modifications of the matrix model.
Chen Yi-Xin
Gould Mark D.
Zhang Yao-Zhong
No associations
LandOfFree
Finite matrix model of quantum Hall fluids on $S^2$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Finite matrix model of quantum Hall fluids on $S^2$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Finite matrix model of quantum Hall fluids on $S^2$ will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-685829