Turning bosons into fermions: exclusion statistics, fractional statistics and the simple harmonic oscillator

Abstract

Motivated by Haldane's exclusion statistics, we construct creation and annihilation operators for g-ons using a bosonic algebra. We find that g-ons appear due to the breaking of a descrete symmetry of the original bosonic system. This symmetry is intimately related to the braid group and we demonstrate a link between exclusion statistics and fractional statistics. *

Statistical correlations in an ideal gas of particles obeying fractional exclusion statistics

“…More recently, an analytic, monotonic relation g = g(α) has been derived in Ref. [23] in the case g = 1/m (for integer m), which is relevant for the fractional quantum Hall effect (see also Ref. [24] for a review).…”

Many-body constraints and non-thermal behavior in 1D open systems with Haldane exclusion statistics

“…This secondquantized description gives an appealingly simple picture of the constraints, in terms of multiple flavors of fermions that are restricted to respect a particular pseudospin ordering in energy space. Though other frameworks for second quantization of particles with novel exclusion statistics exist [56][57][58][59] , ours has the advantage of allowing a straightforward computation of matrix elements, with projections that are easily implemented numerically. As such, this formalism may be useful for investigating the impact of inter-occupancy constraints on other aspects of HES systems.…”

“…Here we develop such a formalism, based on the exact description of the constrained Hilbert space described in Sec. III C. Though other protocols for second quantization of HES particles [56][57][58][59] have been proposed, to the best of our knowledge ours is the first that exactly captures the occupancy constraints.…”

Statistical correlations of an anyon liquid at low temperatures

“…While the former characterisation, corresponding to exchange fractional statistics, applies to dimensions d 2 only, the latter characterisation, corresponding to exclusion statistics, does not suffer from such a restriction, and has been considered for arbitrary dimensionality. The relation between the two definitions of fractional statistics is not completely settled, to date [7]. * In this context, it has been recently proposed that topological excitations such as vortex rings (anyonic loops) in the three-dimensional chiral spin liquids may obey fractional non-Abelian statistics [8].…”