2014/05/31 by N. Cirilo António, N. Manojlović, Igor Salom +1 · 3 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #Quantum many-body systems #hep-th #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1016/j.nuclphysb.2014.10.014
published as Nuclear Physics B 889 (2014) 87-108 · 31 pages; typos corrected
arxiv created 2014/08/14 · openalex publication_date 2014/10/15 · arxiv updated 2014/10/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01
We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the case when both boundary matrices can be brought to the upper-triangular form. We define the Bethe vectors which yield the strikingly simple expression for the off shell action of the transfer matrix, deriving the spectrum and the relevant Bethe equations. We explore further these results by obtaining the off shell action of the generating function of the Gaudin Hamiltonians on the corresponding Bethe vectors through the so-called quasi-classical limit. Moreover, this action is as simple as it could possibly be, yielding the spectrum and the Bethe equations of the Gaudin model.