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]].

70 pages; v2: one figure and a few sentences are added to the introduction; v3: a reference added

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• Hybrid NLIE for the Mirror AdS_5 x S^5
• Quantum groups and functional relations for higher rank
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• Dissipation-driven integrable fermionic systems: from graded Yangians to exact nonequilibrium steady states
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• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
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• Universal Baxter TQ-relations for open boundary quantum integrable systems
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• Evaluation of the operatorial Q-system for non-compact super spin chains
• Transfer matrices of rational spin chains via novel BGG-type resolutions
• Folding QQ-relations and transfer matrix eigenvalues: towards a unified approach to Bethe ansatz for super spin chains
• Quantum groups and functional relations for arbitrary rank
• Integrable systems and AdS/CFT duality
• On Baxter's Q operator of the higher spin XXZ chain at the Razumov-Stroganov point
• Boson-Fermion correspondence, QQ-relations and Wronskian solutions of the T-system