Phase diagram of S = 1 XXZ chain in a staggered magnetic field is obtained numerically. The Berezinskii-Kosterlitz-Thouless transition between the XY and the ant antiferromagnetic phases is studied by the level-spectroscopy. Moreover we find that there is no distinction between the Haldane and the antiferromagnetic phases, since the Gaussian critical line does not appear, in contrast to the S = 1/2 case. It is expected that some hidden Z2 × Z2 symmetry breaking happens not only in the Haldane phase but also in the antiferromagnetic one.
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