Solutions of the T-system and Baxter equations for supersymmetric spin chains

Abstract

We propose Wronskian-like determinant formulae for the Baxter Q -functions and the eigenvalues of transfer matrices for spin chains related to the quantum affine superalgebra U q ( gl ˆ ( M | N ) ) . In contrast to the supersymmetric Bazhanov–Reshetikhin formula (the quantum supersymmetric Jacobi–Trudi formula) proposed in [Z. Tsuboi, J. Phys. A: Math. Gen. 30 (1997) 7975], the size of the matrices of these Wronskian-like formulae is less than or equal to M + N . Base on these formulae, we give new expressions of the solutions of the T-system (fusion relations for transfer matrices) for supersymmetric spin chains proposed in the above-mentioned paper. Baxter equations also follow from the Wronskian-like formulae. They are finite order linear difference equations with respect to the Baxter Q -functions. Moreover, the Wronskian-like formulae also explicitly solve the functional relations for Bäcklund flows proposed in [V. Kazakov, A. Sorin, A. Zabrodin, Nucl. Phys. B790 (2008) 345, arXiv:hep-th/0703147].