Towards the solution of an integrable $D_2^{(2)}$ spin chain

Abstract

Two branches of integrable open quantum-group invariant $D_{n+1}^{(2)}$ quantum spin chains are known. For one branch (epsilon=0), a complete Bethe ansatz solution has been proposed. However, the other branch (epsilon=1) has so far resisted solution. In an effort to address this problem, we consider here the simplest case n=1. We propose a Bethe ansatz solution, which however is not complete, as it describes only the transfer-matrix eigenvalues with odd degeneracy. We also consider a proposal for the missing eigenvalues.

arXiv comment18 pages; v2: added author Rodrigo A. Pimenta, Section 5, and appendix

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Cited by in corpus (10)

• Integrable boundary conditions in the antiferromagnetic Potts model
• Lattice regularisation of a non-compact boundary conformal field theory
• Spectrum of the quantum integrable $D_2^{(2)}$ spin chain with generic boundary fields
• Exact solution of the quantum integrable model associated with the twisted $D_3^{(2)}$ algebra
• The $D_3^{(2)}$ spin chain and its finite-size spectrum
• Spectrum of the transfer matrices of the spin chains associated with the $A_3^{(2)}$ Lie algebra
• 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
• A Passion for Theoretical Physics: a special issue in memory of Peter G. O. Freund