Abstract
In this paper, we study a solvable SU(4) spin ladder with Dzyaloshinkii-Moriya interaction along the rung direction. Due to the rung anisotropy, the rung spin triplet is splitted into a singlet and a doublet. This splitting leads to some quantum phase transitions and the magnetization plateaus, with or without spin gap. Exact phase diagram and magnetization plateaus are presented based on the Bethe ansatz solutions. A magnetization line with $〈M〉=1/3$ is found in the Ising limit.
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