The integrable quantum group invariant A_{2n-1}^(2) and D_{n+1}^(2) open spin chains

Abstract

A family of A_{2n}^(2) integrable open spin chains with U_q(C_n) symmetry was recently identified in arXiv:1702.01482. We identify here in a similar way a family of A_{2n-1}^(2) integrable open spin chains with U_q(D_n) symmetry, and two families of D_{n+1}^(2) integrable open spin chains with U_q(B_n) symmetry. We discuss the consequences of these symmetries for the degeneracies and multiplicities of the spectrum. We propose Bethe ansatz solutions for two of these models, whose completeness we check numerically for small values of n and chain length N. We find formulas for the Dynkin labels in terms of the numbers of Bethe roots of each type, which are useful for determining the corresponding degeneracies. In an appendix, we briefly consider D_{n+1}^(2) chains with other integrable boundary conditions, which do not have quantum group symmetry.

47 pages; v2: two references added and minor changes

References in corpus (2)

• Quantum spin transistor with a Heisenberg spin chain
• Quantum group symmetries and completeness for A_{2n}^(2) open spin chains

Cited by in corpus (12)

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• Surveying the quantum group symmetries of integrable open spin chains
• Towards the solution of an integrable $D_2^{(2)}$ spin chain
• New D_{n+1}^(2) K-matrices with quantum group symmetry
• Integrable boundary conditions for staggered vertex models
• The spectrum of quantum-group-invariant transfer matrices
• Exact solution of the quantum integrable model associated with the twisted $D_3^{(2)}$ algebra
• Exact solution of the $q$-deformed $D_3^{(1)}$ vertex model with open boundaries
• Spectrum of the transfer matrices of the spin chains associated with the $A_3^{(2)}$ Lie algebra
• Factorization identities and algebraic Bethe ansatz for $D_2^{(2)}$ models