‘‘Fractional statistics’’ in arbitrary dimensions: A generalization of the Pauli principle

F. D. M. Haldane
Phys. Rev. Lett. 67, 937 – Published 19 August 1991
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Abstract

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.

  • Received 19 March 1991

DOI:https://doi.org/10.1103/PhysRevLett.67.937

©1991 American Physical Society

Authors & Affiliations

F. D. M. Haldane

  • Department of Physics, Princeton University, Princeton, New Jersey 08544

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Issue

Vol. 67, Iss. 8 — 19 August 1991

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