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}(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]].
Cite
@article{arxiv.0906.2039,
title = {Solutions of the T-system and Baxter equations for supersymmetric spin chains},
author = {Zengo Tsuboi},
journal= {arXiv preprint arXiv:0906.2039},
year = {2010}
}
Comments
70 pages; v2: one figure and a few sentences are added to the introduction; v3: a reference added