The spectrum of quantum-group-invariant transfer matrices

Abstract

Integrable open quantum spin-chain transfer matrices constructed from trigonometric R-matrices associated to affine Lie algebras $\hat{g}$, 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 p-th node from the $\hat{g}$ 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.

37 pages

References in corpus (5)

• Non compact conformal field theory and the a_2^{(2)} (Izergin-Korepin) model in regime III
• Nonstandard Bethe Ansatz equations for open O(N) spin chains
• Surveying the quantum group symmetries of integrable open spin chains
• The integrable quantum group invariant A_{2n-1}^(2) and D_{n+1}^(2) open spin chains
• Quantum group symmetries and completeness for A_{2n}^(2) open spin chains

Cited by in corpus (8)

• Introduction to classical and quantum integrability
• Towards the solution of an integrable $D_2^{(2)}$ spin chain
• Spectrum of the quantum integrable $D_2^{(2)}$ spin chain with generic boundary fields
• Exact surface energy of the $D_2^{(1)}$ spin chain with generic non-diagonal boundary reflections
• Spin chains with boundary inhomogeneities
• Exact physical quantities of the $D_2^{(2)}$ spin chain model with generic open boundary conditions
• Quantum-group-invariant $D_{n+1}^{(2)}$ models: Bethe ansatz and finite-size spectrum
• Factorization identities and algebraic Bethe ansatz for $D_2^{(2)}$ models