2017/05/31 by N. Manojlović, Igor Salom, and I. Salom · 1 citation
Mathematics · Physics and Astronomy · #Algebraic number #Algebraic structures and combinatorial models #Bethe ansatz #Black Holes and Theoretical Physics #Boundary (topology) #Chain (unit) #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Nonlinear Waves and Solitons #Physics #Quantum mechanics #Spin (aerodynamics) #Transfer matrix #Trigonometry #hep-th #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1016/j.nuclphysb.2017.07.017
published as Nuclear Physics B 923 (2017) pp. 73-106 · 39 pages. Typos corrected. arXiv admin note: substantial text overlap with arXiv:1405.7398, arXiv:1412.1396
openalex created_date 2017/05/19 · openalex publication_date 2017/08/03 · arxiv created 2017/08/18 · arxiv updated 2017/08/21 · openalex updated_date 2026/08/05
The implementation of the algebraic Bethe ansatz for the XXZ Heisenberg spin chain in the case, when both reflection matrices have the upper-triangular form is analyzed. The general form of the Bethe vectors is studied. In the particular form, Bethe vectors admit the recurrent procedure, with an appropriate modification, used previously in the case of the XXX Heisenberg chain. As expected, these Bethe vectors yield the strikingly simple expression for the off-shell action of the transfer matrix of the chain as well as the spectrum of the transfer matrix and the corresponding Bethe equations. As in the XXX case, the so-called quasi-classical limit gives the off-shell action of the generating function of the corresponding trigonometric Gaudin Hamiltonians with boundary terms.