Quantum Hall Fluid on Fuzzy Two Dimensional Sphere

LUO Xu-Dong; PENG Dan-Tao

Chinese Physics C> 2004, Vol. 28> Issue(10) : 1040-1044

Quantum Hall Fluid on Fuzzy Two Dimensional Sphere

LUO Xu-Dong ^, ,
PENG Dan-Tao

Institute of Modern Physics,Northwest University,Xi'an 710069,China

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After reviewing the Haldane's description about the quantum Hall effect on the fuzzy two sphere S², we construct the noncommutative algebra on the fuzzy sphere S² and the Moyal structure of the Hilbert space. By constructing noncommutative Chern Simons theory of the incompressible Hall fluid on the fuzzy sphere and solving the Gaussian constraint with quasiparticle source, we find the Calogero matrix on S² and the complete set of the Laughlin wave function for the lowest Landau level, and this wave function is expressed by the generalized Jack polynomials in terms of spinor coordinates.

References

[1]

. Laughlin R B. Phys. Rev. Lett ., 1983, 50: 1395 —13982. Haldane F D M. Phys. Rev. Lett., 1983, 51: 605 —6083. Susskind L. The Quantum Hall Fluid and Non-Commutative Chern-Si-mons Theory. hep-th/ 01010294. Berneving B A, Brodie J, Susskind L et al. JHEP, 2001, 02: 0035. ZHANG Shou-Cheng, HU Jiang-Ping. Science, 2001, 294: 823 —8286. HU Jiang-Ping, ZHANG Shou-Cheng. Phys. Rev., 2002, B66: 125301 —1253107. Polychronakos A P. JHEP, 2001, 04: 0118. Morariu B, Polychronakos A P. JHEP, 2001, 07: 0069. Hellerman S, Raamsdonk M V. JHEP, 2001, 10: 03910. Karabali D, Sakita B. Phys. Rev., 2002, B65: 075304 —07530811. Fabinger M. JHEP, 2002, 05: 03712. CHEN Yi-Xin, HOU Bo-Yu, HOU Bo-Yuan. Nucl. Phys., 2002, B638: 220 —24213. Polychronakos A P. JHEP, 2001, 06: 07014. HOU Bo-Yu, PENG Dan-Tao, SHI Kang-Jie et al. Int. J. Mod. Phys., 2003, A18: 2477 —250015. HOU Bo-Yu, HOU Bo-Yuan, YUE Rui-Hong. J. Phys., 2002, A35: 2937 —294616. Seiberg N, Witten E. JHEP, 1999, 09: 03217. Alekseev A, Recknagel A, Schomerus V. JHEP, 1999, 09: 02318. Perelomov. Generalized Coherent States and Their Applications. Berlin: Springer, 198619. Chan Chuan-Tsung, CHEN Chiang-Mei, LIN Feng-Li et al. Nucl. Phys., 2002, B625: 327 —34420. Gilmore R. Lie Groups, Lie Algebras, and Some of Their Applications. New York: a Wiley-Interscience Publication, 197421. Hurtubise J C, Markman E. Comm. Math. Phys., 2001, 223: 533 —55222. Bordner A J, Manton N S, Sasaki R. Prog. Theor. Phys, 2000, 103: 463 —48723. Bordner A J, Corrigan E, Sasaki R. Prog. Theor. Phys., 1998, 100: 1107 —112924. Nishino A, Ujino H , Wadati M. Symmetric Fock Space and OrthogonalSymmetric Polynomials Associated With the Calogero Model. cond2-mat/980328425. Atiyah M F. Geometry of Yang-Mills Fields. Pisa: Accademia Nazionale del Lincei, 197926. Hanany A, Witten E. Nucl. Phys., 1997, B492: 152 —190

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LUO Xu-Dong and PENG Dan-Tao. Quantum Hall Fluid on Fuzzy Two Dimensional Sphere[J]. Chinese Physics C, 2004, 28(10): 1040-1044.

LUO Xu-Dong and PENG Dan-Tao. Quantum Hall Fluid on Fuzzy Two Dimensional Sphere[J]. Chinese Physics C, 2004, 28(10): 1040-1044. shu

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Received: 2004-03-08
Revised: 1900-01-01

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通讯作者: 陈斌, bchen63@163.com

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沈阳化工大学材料科学与工程学院沈阳 110142

Quantum Hall Fluid on Fuzzy Two Dimensional Sphere

Corresponding author: LUO Xu-Dong,

Institute of Modern Physics,Northwest University,Xi'an 710069,China

Received Date: 2004-03-08

Accepted Date: 1900-01-01

Available Online: 2004-10-05

Abstract: After reviewing the Haldane's description about the quantum Hall effect on the fuzzy two sphere S², we construct the noncommutative algebra on the fuzzy sphere S² and the Moyal structure of the Hilbert space. By constructing noncommutative Chern Simons theory of the incompressible Hall fluid on the fuzzy sphere and solving the Gaussian constraint with quasiparticle source, we find the Calogero matrix on S² and the complete set of the Laughlin wave function for the lowest Landau level, and this wave function is expressed by the generalized Jack polynomials in terms of spinor coordinates.

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Quantum Hall Fluid on Fuzzy Two Dimensional Sphere

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