Charge and statistics of quantum Hall quasi-particles - A numerical study of mean values and fluctuations

Nuclear Physics B

Volumn 559, Issue 3, 1999, Pages 705-742

  Kjonsberg H ^a   Leinaas, J M ^a  

^a UNIVERSITY OF OSLO   (Norway)

Author keywords

Quantum hall effect; Quasi particles

Indexed keywords

EID: 0033604221     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(99)00353-3     Document Type: Article

References (25)

1. V.J. Goldman and B. Su, Resonant tunneling in the quantum hall regime: Measurement of fractional charge, Science 267 (1995) 1010; L. Saminadayer, D.C. Glattli, Y. Jin and B. Etienne, Observation of the e/3 fractionally charged Laughlin quasiparticles, Phys. Rev. Lett. 79 (1997) 2526; R. De-Picciotto, M. Reznikov, M. Heiblum, V. Umansky, G. Bunin and D. Mahalu, Direct observation of a fractional charge, Nature 389 (1997) 162.
2. V.J. Goldman and B. Su, Resonant tunneling in the quantum hall regime: Measurement of fractional charge, Science 267 (1995) 1010; L. Saminadayer, D.C. Glattli, Y. Jin and B. Etienne, Observation of the e/3 fractionally charged Laughlin quasiparticles, Phys. Rev. Lett. 79 (1997) 2526; R. De-Picciotto, M. Reznikov, M. Heiblum, V. Umansky, G. Bunin and D. Mahalu, Direct observation of a fractional charge, Nature 389 (1997) 162.
3. V.J. Goldman and B. Su, Resonant tunneling in the quantum hall regime: Measurement of fractional charge, Science 267 (1995) 1010; L. Saminadayer, D.C. Glattli, Y. Jin and B. Etienne, Observation of the e/3 fractionally charged Laughlin quasiparticles, Phys. Rev. Lett. 79 (1997) 2526; R. De-Picciotto, M. Reznikov, M. Heiblum, V. Umansky, G. Bunin and D. Mahalu, Direct observation of a fractional charge, Nature 389 (1997) 162.
4. R.B. Laughlin, Anomalous quantum hall effect: An incompressible quantum fluid with fractionally charged excitations, Phys. Rev. Lett. 50 (1983) 1395.
5. D. Arovas, J.R. Schriffer and F. Wilczek, Fractional statistics and the quantum hall effect, Phys. Rev. Lett. 53 (1984) 722.
6. J.K. Jain, Composite-fermion approach for the fractional quantum hall effect, Phys. Rev. Lett. 63 (1989) 199.
7. H. Kjønsberg and J.M. Leinaas, On the anyon description of the Laughlin hole states, Int. J. Mod. Phys. A 12 (1997) 1975.
8. H. Kjønsberg and J. Myrheim, Numerical study of charge and statistics of Laughlin quasi-particles, Int. J. Mod. Phys. A 14 (1999) 537.
9. S. Kivelson and M. Roček, Consequences of gauge invariance for fractionally charged quasi-particles, Phys. Lett. B 156 (1985) 85.
10. S. Kivelson and J.R. Schrieffer, Fractional charge, a sharp quantum observable, Phys. Rev. B 25 (1982) 6447.
11. R. Rajaraman and J.S. Bell, On solitons with half integral charge, Phys. Lett. B 116 (1982) 151.
12. A.S. Goldhaber and S. Kivelson, Local charge versus Aharonov-Bohm charge, Phys. Lett. B 255 (1991) 445.
13. F. James, Monte Carlo theory and practice, Rep. Prog. Phys. 43 (1980) 1145.
14. R.B. Laughlin, in The Quantum Hall Effect ed. R.E. Prange and S.M. Girvin (Springer, Berlin, 1990).
15. R. Morf and B.I. Halperin, Monte Carlo evaluation of trial wave functions for the fractional quantized hall effect: Disk geometry, Phys. Rev. B 33 (1986) 2221.
16. F.D.M. Haldane and E.H. Rezayi, Finite-size studies of the incompressible state of the fractionally quantized hall effect and its excitations, Phys. Rev. Lett. 54 (1985) 237.
17. N. Trivedi and J.K. Jain, Numerical study of Jastrow-Slater trial states for the fractional quantum hall effect, Mod. Phys. Lett. B 5 (1991) 503.
18. S.M. Girvin and T. Jach, Formalism for the quantum hall effect: Hilbert space of analytic functions, Phys. Rev. B 29 (1984) 5617.
19. W.H. Press, W.T. Vetterling, S.A. Teukolsky and B.P. Flannery, Numerical Recipes in C, (Cambridge Univ. Press, Cambridge, 1992).
20. M.B. Berry, Quantal phase factors accompanying adiabatic changes, Proc. R. Soc. Lond. A. 392 (1984) 45.
21. Y. Aharonov and D. Bohm, Significance of electromagnetic potentials in the quantum theory, Phys. Rev. 115 (1959) 485.
22. T.H. Hansson, J.M. Leinaas and J. Myrheim, Dimensional reduction in anyon systems, Nucl. Phys. B 384 (1992) 559.
23. F.D.M. Haldane, Fractional statistics in arbitrary dimensions: A generalization of the Pauli principle, Phys. Rev. Lett. 67 (1991) 937.
24. G. Dev and J.K. Jain, Jastrow-Slater trial wave functions for the fractional quantum hall effect: Results for few-particle systems, Phys. Rev. B 45 (1992) 1223.
25. M.D. Johnson and G.S. Canright, Haldane fractional statistics in the fractional quantum hall effect, Phys. Rev. B 49 (1994) 294 7.