The idea of abelian Chern-Simons theory as an effective field theory exhibiting the fractional quantum Hall effect (abelian topological order) goes back to
Steven M. Girvin, around (10.7.15) in: Summary, Omissions and Unanswered Questions, Chapter 10 of: The Quantum Hall Effect, Graduate Texts in Contemporary Physics, Springer (1986, 1990) [doi:10.1007/978-1-4612-3350-3]
Steven M. Girvin, A. H. MacDonald, around (10) of: Off-diagonal long-range order, oblique confinement, and the fractional quantum Hall effect, Phys. Rev. Lett. 58 12 (1987) (1987) 1252-1255 [doi:10.1103/PhysRevLett.58.1252]
Shou Cheng Zhang, T. H. Hansson S. Kivelson: Effective-Field-Theory Model for the Fractional Quantum Hall Effect, Phys. Rev. Lett. 62 (1989) 82 [doi:10.1103/PhysRevLett.62.82]
and was made more explicit in:
Xiao-Gang Wen, Anthony Zee: Quantum statistics and superconductivity in two spatial dimensions, Nuclear Physics B – Proceedings Supplements 15 (1990) 135-156 [doi:10.1016/0920-5632(90)90014-L]
B. Blok, Xiao-Gang Wen: Effective theories of the fractional quantum Hall effect at generic filling fractions, Phys. Rev. B 42 (1990) 8133 [doi:10.1103/PhysRevB.42.8133]
Jürg Fröhlich, T. Kerler: Universality in quantum Hall systems, Nuclear Physics B 354 2–3 (1991) 369-417 [doi:10.1016/0550-3213(91)90360-A]
Jürg Fröhlich, Anthony Zee: Large scale physics of the quantum hall fluid, Nuclear Physics B 364 3 (1991) 517-540 [doi:10.1016/0550-3213(91)90275-3]
Z. F. Ezawa, A. Iwazaki: Chern-Simons gauge theories for the fractional-quantum-Hall-effect hierarchy and anyon superconductivity, Phys. Rev. B 43 (1991) 2637 [doi:10.1103/PhysRevB.43.2637]
A. P. Balachandran, A. M. Srivastava: Chern-Simons Dynamics and the Quantum Hall Effect [arXiv:hep-th/9111006, spire:319826]
Ana Lopez, Eduardo Fradkin: Fractional quantum Hall effect and Chern-Simons gauge theories, Phys. Rev. B 44 (1991) 5246 [doi:10.1103/PhysRevB.44.5246]
Xiao-Gang Wen, Anthony Zee: Topological structures, universality classes, and statistics screening in the anyon superfluid, Phys. Rev. B 44 (1991) 274 [doi:10.1103/PhysRevB.44.274]
Xiao-Gang Wen, Anthony Zee: Classification of Abelian quantum Hall states and matrix formulation of topological fluids, Phys. Rev. B 46 (1992) 2290 [doi:10.1103/PhysRevB.46.2290]
Xiao-Gang Wen, Anthony Zee: Shift and spin vector: New topological quantum numbers for the Hall fluids, Phys. Rev. Lett. 69 (1992) 953, Erratum Phys. Rev. Lett. 69 3000 (1992) [doi:10.1103/PhysRevLett.69.953]
Xiao-Gang Wen: Theory of Edge States in Fractional Quantum Hall Effects, International Journal of Modern Physics B 06 10 (1992) 1711-1762 [doi:10.1142/S0217979292000840]
A. P. Balachandran, L. Chandar, B. Sathiapalan: Chern-Simons Duality and the Quantum Hall Effect, Int. J. Mod. Phys. A11 (1996) 3587-3608 [doi:10.1142/S0217751X96001693, arXiv:hep-th/9509019]
Early review:
Shou Cheng Zhang: The Chern-Simons-Landau-Ginzburg theory of the fractional quantum Hall effect, International Journal of Modern Physics B 06 01 (1992) 25-58 [doi:10.1142/S0217979292000037, pdf]
Anthony Zee: Quantum Hall Fluids, in: Field Theory, Topology and Condensed Matter Physics, Lecture Notes in Physics 456, Springer (1995) [doi:10.1007/BFb0113369, arXiv:cond-mat/9501022]
Xiao-Gang Wen: Topological orders and Edge excitations in FQH states, Advances in Physics 44 5 (1995) 405 [doi:10.1080/00018739500101566, arXiv:cond-mat/9506066]
Further review and exposition:
Yuan-Ming Lu, Ashvin Vishwanath, part II of: Theory and classification of interacting integer topological phases in two dimensions: A Chern-Simons approach, Phys. Rev. B 86 (2012) 125119, Erratum Phys. Rev. B 89 (2014) 199903 [doi:10.1103/PhysRevB.86.125119, arXiv:1205.3156]
Eduardo Fradkin, chapter 7 of: Field Theories of Condensed Matter Physics, Cambridge University Press (2013) [doi:10.1017/CBO9781139015509, ISBN:9781139015509]
Edward Witten, pp 30 in: Three Lectures On Topological Phases Of Matter, La Rivista del Nuovo Cimento 39 (2016) 313-370 [doi:10.1393/ncr/i2016-10125-3, arXiv:1510.07698]
David Tong §5 of: The Quantum Hall Effect, lecture notes (2016) [arXiv:1606.06687, course webpage, pdf, pdf]
Josef Wilsher: The Chern–Simons Action & Quantum Hall Effect: Effective Theory, Anomalies, and Dualities of a Topological Quantum Fluid, PhD thesis, Imperial College London (2020) [pdf]
For discussion of the fractional quantum Hall effect via abelian but noncommutative (matrix model-)Chern-Simons theory
On edge modes:
Further developments:
Dmitriy Belov, Gregory W. Moore, §7 of: Classification of abelian spin Chern-Simons theories [arXiv:hep-th/0505235]
Christian Fräßdorf: Abelian Chern-Simons Theory for the Fractional Quantum Hall Effect in Graphene, Phys. Rev. B 97 115123 (2018) [doi:10.1103/PhysRevB.97.115123, arXiv:1712.03595]
Kristan Jensen, Amir Raz: The Fractional Hall hierarchy from duality [arXiv:2412.17761]
Abhishek Agarwal, Dimitra Karabali, V.P. Nair: Fractional quantum Hall effect in higher dimensions [arXiv:2410.14036]
Last revised on January 28, 2025 at 13:04:27. See the history of this page for a list of all contributions to it.