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Magnetization curve and correlation function of Haldane-gap antiferromagnet in strong magnetic field

The shape of the magnetization curve of the S =1 Heisenberg antiferromagnet at zero temperature is discussed. It is found that the magnetization behaves as \(\sqrt{h-h_{c}}\) at the beginning of magnetization as a function of external field h . The transverse correlation function = of this system decays algebraically at zero temperature when it is partially magnetized by the field to the z -direction ( ≃(-1) n n -η ). The exponent η is 0.3∼0.5. This exponent can be calculated by the Luttinger liquid assumption and diagonalization results of finite chains. This is in contrast to the exponential decay of this chain in zero field.