Abstract
Back in 1982, when condensed matter physicists were slowly recovering from the shock produced by the discovery of the (integer) Quantum Hall Effect (IQHE) two years earlier [1], a new surprise came in a paper by Tsui, Stornier, and Gossard [2], who reported quantized Hall plateaus at filling factors v = 1/3 and v = 2/3 (see Fig. 1). This finding opened the vast field of exciting studies of the Fractional Quantum Hall Effect (FQHE), in which many new surprises were to come.
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References
von Klitzing, K., Dorda, and Pepper, M. (1980) Phys. Rev. Lett. 45, 494.
Tsui, D.C., Stornier, H.L. and Gossard, A.C. (1982) Phys. Rev. Lett. 48, 1559.
Yoshioka, D. and Lee, P.A. (1983) Phys. Rev. B 27, 4986
Laughlin, R. (1983) Phys. Rev. Lett. 50, 1395.
Su W.P. and Schrieffer, J.R. (1981) Phys. Rev. Lett. 46, 738.
Stornier, H.L.(1992) Physica B 177, 401.
Du, R.R., Stornier, H.L., Tsui, D.C., Pfeiffer, L.N., and West, K.W. (1993) 2944.
Haidane, F.D.M. (1983) Phys. Rev. Lett. 51, 605.
Jain, J.K. (1989) Phys. Rev. Lett. 63, 199, (1989) Phys. Rev. B 40, 8079, (1990) Phys. Rev. B 41, 7653.
Lopez, A. and Fradkin, E. (1991) Phys. Rev. B 44, 5246 ibid 47, 7080.
Kalmeyer, V. and Zhang, S.-C. (1992). Phys. Rev. B 46, 9889.
Halperin, B.I.P., Lee, A. and N. Read, (1993) Phys. Rev. B 47, 7312.
Willet, R.L. (1997) Adv. Phys. 46, 447.
Composite Fermions, Edited by O. Heinonen, World Scientific, Singapore (1998).
Simon, S.H.(1998) The Chern-Simons Fermi Liquid Descriptio Franctional Quantum Hall States, ibid; LANL e-print,cond-mat/0108271
Shankar, R. (2001) Theories of the Fractional Quantum Hall Effect, LANL e-print, condmat/0108271.
Extensive numerical calculations, showing an excellent overlap (such as 0.9999) of the Laughlin function with the v=l/3, 1/5 ground states obtained by exact diagonalization, convince us that the Laughlin function is the exact ground state at N→∞ for a wide class of repulsive potentials. However nobody has been able to show this analytically, except for a special short-range potential, when it gives the exact ground state for arbitrary N.
Morf, R. d’Ambrumenil, N., and Halperin, B.I. (1986) Phys. Rev. B 34, 3037.
d’Ambrumenil, N. and Morf, R. (1989) Phys. Rev. B 40, 6108.
Yoshioka, D., MacDonald, A.H., and Girvin, S.M. (1988).Phys. Rev. B 38, 3636
Ginocchio, J.N. and Haxton, W.C. (1996). Phys. Rev. Lett. 77, 1568.
Yannouleas, C. and Landman, U. (2002) LANL e-print, cond-mat/0202062.
Jain, J.K. and Kamilla, R.K (1997) Phys. Rev. B 55, 4895.
Read, N. (1998) Phys. Rev. B 58,16262
Dyson, F.J. (1962) J. Math. Phys. 3, 140.
Mehta, M.L. (1991) Random Matrices, Academic press.
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Dyakonov, M.I. (2003). Twenty Years Since the Discovery of the Fractional Quantum Hall Effect. In: Vagner, I.D., Wyder, P., Maniv, T. (eds) Recent Trends in Theory of Physical Phenomena in High Magnetic Fields. NATO Science Series, vol 106. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0221-9_7
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