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

TL;DR

This paper introduces a graded off-diagonal Bethe ansatz method for solving supersymmetric quantum integrable models, successfully applying it to the $SU(2|2)$ spin chain with various boundary conditions, and deriving explicit eigenvalues.

Contribution

The paper develops a new graded off-diagonal Bethe ansatz approach for supersymmetric models and applies it to solve the $SU(2|2)$ spin chain with generic boundaries.

Findings

Derived eigenvalues via $T-Q$ relations for the $SU(2|2)$ model

Generalized fusion techniques to supersymmetric cases

Method applicable to other high-rank supersymmetric models

Abstract

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.