In this paper, based on the formulation of O (3) non-linear model, we study two dimensional−flux Hubbard model at half-filling. A quantum non-magnetic insulator is explored near metalinsulator transition that may be a possible candidate of spin liquid state. Such quantum nonmagnetic insulator on square lattice is not induced by frustrations. Instead, it originates from quantum spin fluctuations with relatively small e ective spin-moments. In the strong coupling limit, our results of spin velocity and spin order parameter agree with results obtained from earlier calculations.