2010/10/31 by Vladimir V. Bazhanov, Rouven Frassek, Tomasz Lukowski +2 · 1 citation
Physics and Astronomy · Mathematics · #math-ph #cond-mat.stat-mech #hep-th #math.MP
paper · pdf · doi:10.1016/j.nuclphysb.2011.04.006
published as Nucl.Phys.B850:148-174,2011 · 27 pages, 5 figures; v2: typos fixed, references updated and added
arxiv created 2011/02/28 · arxiv updated 2011/06/13
We develop a new approach to Baxter Q-operators by relating them to the theory of Yangians, which are the simplest examples for quantum groups. Here we open up a new chapter in this theory and study certain degenerate solutions of the Yang-Baxter equation connected with harmonic oscillator algebras. These infinite-state solutions of the Yang-Baxter equation serve as elementary, "partonic" building blocks for other solutions via the standard fusion procedure. As a first example of the method we consider sl(n) compact spin chains and derive the full hierarchy of operatorial functional equations for all related commuting transfer matrices and Q-operators. This leads to a systematic and transparent solution of these chains, where the nested Bethe equations are derived in an entirely algebraic fashion, without any reference to the traditional Bethe ansatz techniques.