Possible Spin-Liquid State in Doped Antiferromagnets

The phase diagram of the copper oxide materials as a function of doping δ is obtained in the framework of t-t - J- J model by using the Schiwinger boson-slave fermion theory. The results show that the both doped holes and quantum fluctuation of spins, which are treated on the same footing, are in favor of the spin-liquid state.