K. Byczuk et J. Spalek, STATISTICAL PROPERTIES AND STATISTICAL INTERACTION FOR PARTICLES WITHSPIN - THE HUBBARD-MODEL IN ONE-DIMENSION AND A STATISTICAL SPIN LIQUID, Physical review. B, Condensed matter, 50(16), 1994, pp. 11403-11408
We derive the statistical distribution functions for the Hubbard chain
with infinite Coulomb repulsion among particles and for the statistic
al spin liquid with an arbitrary magnitude of the local interaction in
momentum space. Haldane's statistical interaction is derived from an
exact solution for each of the two models. In the case of the Hubbard
chain, the charge (holon) and the spin (spinon) excitations decouple c
ompletely and are shown to behave statistically as fermions and bosons
, respectively. In both cases the statistical interaction must contain
several components; a rule for the particles with the internal symmet
ry.