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

Abstract
HTML
Reference
Related

PDF

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.

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

[1]	YU Neng-Jie , TANG Chuan-Xiang , ZHENG Shu-Xin , LI Quan-Feng , GONG Ke . 2-D Beam Profile Measurement Based on CT Algorithm with Rotating Multi-Wire Target. Chinese Physics C, 2005, 29(4): 408-412.
[2]	LUO Shi-Yu , SHAO Ming-Zhu , HU Xi-Duo . Average Field Idea and Single Particle Model for 2 Dimension Crystallization Beams(Ⅰ). Chinese Physics C, 2004, 28(1): 96-99.
[3]	HU Xi-Duo , SHAO Ming-Zhu , LUO Shi-Yu , LIU Yong-Sheng , ZHU De-Hai . Average Field Idea and Single Particle Model for 2 Dimension Crystallization Beams(Ⅱ). Chinese Physics C, 2004, 28(2): 196-199.
[4]	CHEN Tao , LI Zhi-Huan , YE Yan-Lin , JIANG Dong-Xing , HUA Hui , LI Xiang-Qing , GE Yu-Cheng , WANG Quan-Jin , PANG Dan-Yang , DI Zhen-Yu . Study of Two-Dimensional Position Sensitive Silicon Detector. Chinese Physics C, 2003, 27(1): 72-75.
[5]	YAN Jun , TAO Bi-You . A Electric Sine-Gordon Soliton Solution in Two-Dimensional Dilaton Gravity Model. Chinese Physics C, 2003, 27(9): 767-769.
[6]	LIU Yi , DONG Bao-Zhong , WANG Jun , DING Yong-Fan , WU Zhong-Hua , LI Zhi-Hong , LI Kai-Xi , WU Dong . The Establishment of a Synchrotron Radiation Two Dimensional Small Angle X-Ray Scattering Equipment and It′s Application. Chinese Physics C, 2002, 26(1): 87-92.
[7]	LIU Fang , LI Jun-Qing , XING Yong-Zhong . Quantum Classical Correspondence in a 2-Dimensional Deformed Harmonic Oscillator System. Chinese Physics C, 2002, 26(9): 949-954.
[8]	SONG Jian-Jun , LI Xi-Guo . Trace Formula and Periodic Orbits Quantization for Two-Dimensional Integrable System. Chinese Physics C, 2001, 25(10): 958-963.
[9]	Lin Hai , Liu Lianshou . An Analytical Study of One-Dimensional Projection for the Self-Affine Fractal of Two-Dimensional Phase Space. Chinese Physics C, 1996, 20(7): 625-634.
[10]	Lin Hai , Zhang Yang , Liu Lianshou . An Analytic Study of Self-affine Fractal in Two-Dimensional Phase Space of High Energy Collisions. Chinese Physics C, 1996, 20(1): 65-75.
[11]	SU Gang , NIU Yun . THE CANONICAL TRANSFORMATION AND THE SPIN WAVE IN TWO DIMENSIONAL HEISENBERG ANTIFER-ROMAGNETIC SYSTEM. Chinese Physics C, 1990, 14(6): 500-503.
[12]	CHEN Tian-Lun , SUO Cun-Chuan , HUANG Wu-Qun . β FUNCTION FOR SU(3)×SU(3) CHIRAL MODEL ON 2-DIMENSIONAL RANDOM TRIANGLE LATTICE. Chinese Physics C, 1990, 14(8): 700-703.
[13]	CHEN Tian-Lun , HUANG Wu-Qun , JIN Ke , SUO Cun-Chuan . β FUNCTION FOR SU(2)×SU(2) CHIRAL MODEL ON 2-DIMENSIONAL RANDOM TRIANGLE LATTICE. Chinese Physics C, 1989, 13(2): 188-192.
[14]	HUANG Wu-Qun , CHEN Tian-Lun , ZHONG Chao-Wu , LI Zhi-Bing . A MONTE CARLO RENORMALIZATION GROUP STUDY OF A 2-DIMENSIONAL TRIANGULAR LATTICE. Chinese Physics C, 1987, 11(1): 38-43.
[15]	LIU Mao-San , SHI Cai-Tu , CHEN Ren-Huai . MAGNETIC FIELD ANALYSIS OF PERMANENT MAGNET UNDULATOR. Chinese Physics C, 1984, 8(1): 59-68.
[16]	LIU MAO-SAN , WU WEN-TAI , LI SHU-SHEN , LIU YU-CHENG , SHI CAI-TU , ZHOU JIE-MIN . ANALYSIS OF TWO DIMENSIONAL FIELDS OF PERMANENT MAGNETIC MULTIPIECE LINEAR ARRAY SYSTEM. Chinese Physics C, 1982, 6(6): 764-767.
[17]	LIU MAO-SAN , WU WEN-TAI , LI SHU-ZHEN , LIU YU-CHENG , SHI CAI-TU , ZHOU JIE-MIN . PLANAR MULTIPOLE FIELD OF A PERMANENT MAGNET SYSTEM WITH QUASI-SEGMENTED AND TRAPEZOIDAL RING STRUCTURE. Chinese Physics C, 1982, 6(2): 251-254.
[18]	LIU MAO-SAN , WU WEN-TA , I LI SHU-ZHEN , CHEN REN-HUAI . DISTRIBUTION OF 2-DIMENSIONAL FIELD OF PERMANENT MAGNETIC PLANE HEAD QUADRUPOLE AND ITS GEOMETRIC PARAMETER SELECTION. Chinese Physics C, 1981, 5(3): 381-385.
[19]	Liu Mao-san , Chen Ren-huai , Wu Wen-tai , Li Shu-zhen . PLANAR MULTIPOLE FIELD OF A PERMANENT MAGNET SYSTEM WITH MULTI-SEGMENTED RING STRUCTURE. Chinese Physics C, 1980, 4(6): 774-777.
[20]	HUANG TAO , XUE PEI-YOU . THE INFRARED STRUCTURE AND THE ELECTROMAGNETIC FORM FACTORS OF QUANTUM CHROMODYNAMICS IN TWO DIMENSIONS. Chinese Physics C, 1979, 3(2): 188-202.

Access

Get Citation

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

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

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

Article Metric

Article Views(4309)
PDF Downloads(544)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
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.

HTML

Reference (1)

Quantum Hall Fluid on Fuzzy Two Dimensional Sphere

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article