Algebraic Bethe ansatz for the quantum group invariant open XXZ chain at roots of unity

DOI10.1016/j.nuclphysb.2016.06.007zbMath1342.82030arXiv1603.09249OpenAlexW2312730672WikidataQ58202880 ScholiaQ58202880MaRDI QIDQ2631432

Rafael I. Nepomechie, Azat M. Gainutdinov

Publication date: 29 July 2016

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.09249

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Exactly solvable models; Bethe ansatz (82B23) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

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Cites Work

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• Cyclic tridiagonal pairs, higher order Onsager algebras and orthogonal polynomials
• Conformal field theory at central charge \(c=0\): a measure of the indecomposability \((b)\) parameters
• Indecomposability parameters in chiral logarithmic conformal field theory
• Lusztig limit of quantum \(s\ell (2)\) at root of unity and fusion of (1,p) Virasoro logarithmic minimal models
• Yang-Baxter equation and representation theory. I
• Cyclic monodromy matrices for \(sl(n)\) trigonometric \(R\)-matrices
• Completeness of the Bethe ansatz for the six- and eight-vertex models.
• On Bethe vectors for the \(XXZ\) model at roots of unity
• Lattice fusion rules and logarithmic operator product expansions
• The supersymmetric \(t\)-\(J\) model with quantum group invariance.
• Associative-algebraic approach to logarithmic conformal field theories
• QUANTUM ALGEBRA STRUCTURE OF EXACTLY SOLUBLE QUANTUM SPIN CHAINS
• Lattice W-algebras and logarithmic CFTs
• The Jordan structure of two-dimensional loop models
• Counting solutions of the Bethe equations of the quantum group invariant open XXZ chain at roots of unity
• Integrable quantum chain and the representation of the quantum group SU_q(2)
• ON COMMUTANTS, DUAL PAIRS AND NON-SEMISIMPLE ALGEBRAS FROM STATISTICAL MECHANICS
• CYCLIC MONODROMY MATRICES FOR THE R-MATRIX OF THE SIX-VERTEX MODEL AND THE CHIRAL POTTS MODEL WITH FIXED SPIN BOUNDARY CONDITIONS
• Boundary conditions for integrable quantum systems
• The general U_q(sl(2)) invariant XXZ integrable quantum spin chain
• Bethe's equation is incomplete for the \(XXZ\) model at roots of unity
• Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg chain. I: Some fundamental eigenvectors.