Dimensional reduction of U(1) × SU(2) Chern-Simons bosonization: Application to the t-J model Original Research Article

We perform a dimensional reduction of the U(1) × SU(2) Chern-Simons bosonization and we apply it to the t-J model, relevant model for high Tc superconductors. This procedure yields a decomposition of the electron field into the product of two “semionic” fields, i.e. fields obeying abelian braid statistics with statistics parameter θ = 14, one carrying the charge and the other the spin degrees of freedom. A mean-field theory is then shown to reproduce correctly the large-distance behaviour of the correlation functions of the 1D t-J model at t ⪢ J. This results shows that to capture the essential physical properties of the model one needs a specific “semionic” form of spin-charge separation.