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Dimensional reduction of U(1) x SU(2) Chern-Simons bosonization: application to the t-J model

Abstract

We perform a dimensional reduction of the U(1)\times SU(2) Chern--Simons bosonization and apply it to the t-J model, relevant for high T_c superconductors. This procedure yields a decomposition of the electron field into a product of two ``semionic" fields, i.e. fields obeying abelian braid statistics with statistics parameter \theta={1\over 4}, 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 result shows that to capture the essential physical properties of the model one needs a specific ``semionic" form of spin--charge separation

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