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

2009/06/30 by Zengo Tsuboi · 2 citations
Physics and Astronomy · Mathematics · #math-ph #cond-mat.stat-mech #hep-th #math.MP #nlin.SI #msc:17B80 #msc:82B23 #msc:81T40 #msc:81R50

paper · pdf · doi:10.1016/j.nuclphysb.2009.08.009

published as Nucl.Phys.B826:399-455,2010 · 70 pages; v2: one figure and a few sentences are added to the introduction; v3: a reference added

arxiv created 2010/01/06 · arxiv updated 2010/01/07

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(hatgl(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]].

Citations

• Supersymmetric Bethe Ansatz and Baxter Equations from Discrete Hirota Dynamics

Cited by

• Wronskian solutions of the T-, Q- and Y-systems related to infinite dimensional unitarizable modules of the general linear superalgebra gl(M|N)
• Asymptotic representations and q-oscillator solutions of the graded Yang-Baxter equation related to Baxter Q-operators