One-Dimensional XXZ Model for Particles Obeying Fractional Statistics
  We define one-dimensional particles as non-abelian representations of the symmetric group $S_N$. The exact solution of an $XXZ$ type Hamiltonian built up with such particles is achieved using the coordinate Bethe Ansatz. The Bethe equations show that fractional statistics, effectively, accounts for coupling an external gauge field to an integer statistics' system. 
Luigi Amico, Andreas Osterloh, and Ulrich Eckern