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

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

1996-05-16

arxiv.org/abs/hep-th/9605115v1

Nucl.Phys. B482 (1996) 731-757

Physics

High Energy Physics

High Energy Physics - Theory

31 pages, Plain TeX, no figures

Scientific paper

10.1016/S0550-3213(96)00458-0

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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