The spectrum of quantum-group-invariant transfer matrices

Author(s)

Nepomechie, I, Rafael ; Retore, Ana L. ^{[1, 2]}

Affiliation

^[1] Univ Estadual Paulista, Inst Fis Teor, Rua Dr Bento Teobaldo Ferraz 271, Bloco 2, BR-01140070 Sao Paulo - Brazil

^[2] Nepomechie, Rafael, I, Univ Miami, Phys Dept, POB 248046, Coral Gables, FL 33124 - USA

• Document type: Journal article
• Source: Nuclear Physics B; v. 938, p. 266-297, JAN 2019.
• Web of Science Citations: 0

Abstract

Integrable open quantum spin-chain transfer matrices constructed from trigonometric R-matrices associated to affine Lie algebras (g) over cap, and from certain K-matrices (reflection matrices) depending on a discrete parameter p, were recently considered in arXiv:1802.04864 and arXiv:1805.10144. It was shown there that these transfer matrices have quantum group symmetry corresponding to removing the pth node from the (g) over cap Dynkin diagram. Here we determine the spectrum of these transfer matrices by using analytical Bethe ansatz, and we determine the dependence of the corresponding Bethe equations on p. We propose formulas for the Dynkin labels of the Bethe states in terms of the numbers of Bethe roots of each type. We also briefly study how duality transformations are implemented on the Bethe ansatz solutions. (C) 2018 The Author(s). Published by Elsevier B.V. (AU)

• FAPESP's process: 17/03072-3 - Quantum Group Symmetries for A_(2n-1)^(2) models
• Grantee: Ana Lúcia Retore
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• FAPESP's process: 15/00025-9 - Backlund transformations in integrable hierarchies, solitons and integrable defects
• Grantee: Ana Lúcia Retore
• Support Opportunities: Scholarships in Brazil - Doctorate