The graded off-diagonal Bethe ansatz method is proposed to study supersymmetric quantum integrable models (i.e., quantum integrable models associated with superalgebras). As an example, the exact solutions of the $SU(2|2)$ vertex model with both periodic and generic open boundary conditions are constructed. By generalizing the fusion techniques to the supersymmetric case, a closed set of operator product identities about the transfer matrices are derived, which allows us to give the eigenvalues in terms of homogeneous or inhomogeneous $T-Q$ relations. The method and results provided in this paper can be generalized to other high rank supersymmetric quantum integrable models.

提出了梯度非对角的Bethe ansatz方法来研究超对称量子可积模型（即与超代数相关的量子可积模型）。举例来说，$\mathrm{小号}ü（2|2）$建立了具有周期性和一般开放边界条件的顶点模型。通过将融合技术推广到超对称情况，可以得出关于传递矩阵的一组封闭的算子乘积恒等式，这使我们能够根据齐次或不齐次给出特征值$Ť-问$关系。本文提供的方法和结果可以推广到其他高阶超对称量子可积模型。