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

Graded Off-diagonal Bethe ansatz solution of the $SU(2|2)$ spin chain model with generic integrable boundaries