×

zbMATH — the first resource for mathematics

“Fractional statistics” in arbitrary dimensions: A generalization of the Pauli principle. (English) Zbl 0990.81534
Summary: The concept of “fractional statistics” is reformulated as a generalization of the Pauli exclusion principle, and a definition independent of the dimension of space is obtained. When applied to the vortexlike quasiparticles of the fractional quantum Hall effect, it gives the same result as that based on the braid-group. It is also used to classify spinons in gapless spin-1/2 antiferromagnetic chains as semions. An extensive one-particle Hilbert-space dimension is essential, limiting fractional statistics of this type to topological excitations confined to the interior of condensed matter. The new definition does not apply to “anyon gas” models as currently formulated: A possible resolution of this difficulty is proposed.

MSC:
81S99 General quantum mechanics and problems of quantization
82B03 Foundations of equilibrium statistical mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] J. M. Leinaas, Nuovo Cimento 37B pp 1– (1977) · doi:10.1007/BF02727953
[2] F. Wilczek, Phys. Rev. Lett. 49 pp 957– (1982) · doi:10.1103/PhysRevLett.49.957
[3] B. I. Halperin, Phys. Rev. Lett. 52 pp 1583– (1984) · doi:10.1103/PhysRevLett.52.1583
[4] B. I. Halperin, Phys. Rev. Lett. 52 pp 2390– (1984) · doi:10.1103/PhysRevLett.52.2390.4
[5] R. B. Laughlin, Phys. Rev. Lett. 60 pp 2677– (1988) · doi:10.1103/PhysRevLett.60.2677
[6] F. D. M. Haldane, Phys. Rev. Lett. 66 pp 1529– (1991) · Zbl 0968.82507 · doi:10.1103/PhysRevLett.66.1529
[7] R. B. Laughlin, Phys. Rev. Lett. 50 pp 1359– (1983) · doi:10.1103/PhysRevLett.50.1395
[8] F. D. M. Haldane, Phys. Rev. Lett. 55 pp 2887– (1985) · doi:10.1103/PhysRevLett.55.2887
[9] F. D. M. Haldane, Phys. Rev. Lett. 51 pp 605– (1983) · doi:10.1103/PhysRevLett.51.605
[10] P. W. Anderson, Science 235 pp 1196– (1987) · doi:10.1126/science.235.4793.1196
[11] S. A. Kivelson, Phys. Rev. B 35 pp 8865– (1987) · doi:10.1103/PhysRevB.35.8865
[12] I. Affleck, Nucl. Phys. B265 (1986)
[13] H. A. Bethe, Z. Phys. 71 pp 205– (1931) · doi:10.1007/BF01341708
[14] F. D. M. Haldane, Phys. Rev. Lett. 60 pp 635– (1988) · doi:10.1103/PhysRevLett.60.635
[15] B. S. Shastry, Phys. Rev. Lett. 60 pp 639– (1988) · doi:10.1103/PhysRevLett.60.639
[16] V. Kalmeyer, Phys. Rev. Lett. 59 pp 2095– (1987) · doi:10.1103/PhysRevLett.59.2095
[17] G. S. Canwright, Phys. Rev. Lett. 63 pp 2291– (1989) · doi:10.1103/PhysRevLett.63.2291
[18] P. C. E. Stamp, Europhys. Lett. 14 pp 569– (1991) · doi:10.1209/0295-5075/14/6/012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.