Statistical properties and statistical interaction for particles with spin: Hubbard model in one dimension and statistical spin liquid

TL;DR

This paper derives the statistical distribution functions for particles in one-dimensional Hubbard models and spin liquids, revealing how charge and spin excitations behave statistically as fermions and bosons, respectively.

Contribution

It provides an exact derivation of Haldane's statistical interaction for these models, clarifying the statistical behavior of charge and spin excitations.

Findings

Charge and spin excitations decouple in the Hubbard chain.

Charge behaves as fermions, spin as bosons.

Statistical interaction involves multiple components for particles with internal symmetry.

Abstract

We derive the statistical distribution functions for the Hubbard chain with infinite Coulomb repulsion among particles and for the statistical 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 completely 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 symmetry.