New D_{n+1}^(2) K-matrices with quantum group symmetry

Abstract

We find new families of solutions of the $D_{n+1}^{(2)}$ boundary Yang-Baxter equation. The open spin-chain transfer matrices constructed with these K-matrices have quantum group symmetry corresponding to removing one node from the $D_{n+1}^{(2)}$ Dynkin diagram, namely, $U_q(B_{n-p})\otimes U_q(B_p)$, where $p=0,\dots ,n$. These transfer matrices also have a $p\leftrightarrow n-p$ duality symmetry. These symmetries help to account for the degeneracies in the spectrum of the transfer matrix.

15 pages; v2: minor changes to match the published version. arXiv admin note: text overlap with arXiv:1802.04864

References in corpus (2)

• 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

Cited by in corpus (10)

• Integrable boundary conditions in the antiferromagnetic Potts model
• Lattice regularisation of a non-compact boundary conformal field theory
• Towards the solution of an integrable $D_2^{(2)}$ spin chain
• Finite size spectrum of the staggered six-vertex model with $U_q(\mathfrak{sl}(2))$-invariant boundary conditions
• Integrable boundary conditions for staggered vertex models
• 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
• Exact physical quantities of the $D_2^{(2)}$ spin chain model with generic open boundary conditions
• Spectrum of the transfer matrices of the spin chains associated with the $A_3^{(2)}$ Lie algebra
• Quantum-group-invariant $D_{n+1}^{(2)}$ models: Bethe ansatz and finite-size spectrum