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

TL;DR

This paper introduces new Wronskian-like determinant formulas for Baxter Q-functions and transfer matrix eigenvalues in supersymmetric spin chains, simplifying the solutions of the T-system and Baxter equations.

Contribution

It provides smaller matrix size formulas for supersymmetric spin chain solutions, improving upon previous supersymmetric Jacobi-Trudi formulas.

Findings

New Wronskian-like formulas for Q-functions and transfer matrices

Explicit solutions to the T-system and Baxter equations

Finite order linear difference equations for Baxter Q-functions

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}(hat{gl}(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 abovementioned 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 Backlund flows proposed in [V. Kazakov, A. Sorin, A. Zabrodin, Nucl. Phys. B790 (2008) 345 [arXiv:hep-th/0703147]].