Abstract
On the basis of the method of equation of motion, the ground states of the quantum spin systems with a long-range order are studied. The equations of motion for the spin operators are linearized by introduction of the effective field, which is the order parameter itself. The linearized equations of motion and the use of approximate commutation relations for spin operators lead to the boson representation of the systems. It is emphasized that in the ground state with the long-range order along the x -axis, the relationship ( S j y ) 2 +( S j z ) 2 =1/2 should be retained in the average. By use of the above constraint for spin fluctuations, the values of the long-range order and ground-state energy are calculated within the boson approximation. The results agree well with ones obtained by different methods.
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