Correlated systems of spin-unpolarized fractional quantum Hall effect based on the fermionic Chern-Simons theory

By allowing the spin degrees of freedom we present the Chern-Simons theory for the fractional quantum Hall effect in single layers. Following the Belkhir and Jain's spin-singlet half integral quantum Hall trial wave function, we develop the U(1) x U(1) Chern-Simons theory for nu = 1/2 filling fraction by attaching spin-dependent flux quanta to each electron in the limit of vanishing the Zeeman energy. The Chern-Simons theory is also examined to account for the spin-unpolarized and partially polarized states in single layers. We find from our present theory that all even numerator or even denominator quantum Hall states are unpolarized.