Citation: Haldane, F. Duncan M. " 'Fractional statistics' in arbitrary dimensions: A generalization of the Pauli principle." Physical review letters 67.8 (1991): 937.
Web: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.67.937
Tags: Physical, Abelian-anyons, Foundational, Quantum-hall-effect, Spin-chains
This paper studies a generalization of the Pauli exclusion principle to anyons. The idea is that as anyons are added to a condensed matter system and put on various sites, it will change the number of allowed states that the other anyons can be in. For instance, if a fermion is added to the same site as another fermion it restricts the site because the state vectors of the two fermions must be orthogonal by the Pauli exclusion principle. Two bosons being in the same space does not change the number of degrees of freedom allowed. With anyons, the way that adding different anyon types determines the possible states of anyons becomes more subtle, but it certainly exists. Haldane highlights this theory, and works it out for Laughlin's 1/m states and a spin-1/2 antiferromagnet chain of semions.
An interesting aspect of this work is that it implies that the local Hilbert space of an anyon must have dimension which scales linearly with the system size of the condensed matter physics. This is one of several results in the field which indicate that anyons are "infinite dimensional" phenomena - to be realized perfectly with zero correlation length and no finite size effects, the internal Hilbert space of every anyon must be infinite dimensional. This is a sense in which Bosons and Fermions are quite special.
This generalized Pauli exclusion principle has been dubbed "exclusion statistics", and has since become an important topic in the field, see e.g.
> Ardonne, Eddy, Peter Bouwknegt, and Kareljan Schoutens. "Non-abelian quantum Hall states—exclusion statistics, K-matrices, and duality." Journal of Statistical Physics 102 (2001): 421-469.
> Liu, Dan, et al. "Generalized Pauli principle for particles with distinguishable traits." Physical Review E—Statistical, Nonlinear, and Soft Matter Physics 85.1 (2012): 011144.