The integrable quantum group invariant A 2 n ? 1 ( 2 ) and D n + 1 ( 2 ) open spin chains

摘要

A family of A 2 n ( 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 2 n ? 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.