Integrable higher spin chains with SU-q(2) symmetry

Tetsuo Deguchi, Chihiro Matsui

Nicolas Crampé, Rafael I. Nepomechie, Luc Vinet +1 more

Alexander Nichols

We consider the SU q ( N ) invariant spin chain with diagonal and non-diagonal integrable boundary terms. The algebraic study of spin chains with different kinds of boundary terms is used to motivate a set of spectral equivalences between integrable chains with purely diagonal boundary terms and ones with an arbitrary non-diagonal term at one end. For each choice of diagonal boundary terms there is an iso-spectral one-boundary problem and vice versa. The cases N = 2, 3, 4 are used as examples throughout to illustrate the general structure. The quantum group SU q ( N ) symmetry is broken by the presence of a non-diagonal boundary term; however, one can use the spectral equivalence with the diagonal chain to easily understand the residual symmetries of the system. This is described in detail for the case of SU (3).

P. P. Kulish

P. P. Kulish

Laurens Stronks, Johan W. van de Leur, Dirk Schuricht

Abstract Using the representation theory of Yangians we construct the rational R -matrix which takes values in the adjoint representation of SU( n ). From this we derive an integrable SU( n ) spin chain with lattice spins transforming under the adjoint representation. However, the resulting Hamiltonian is found to be non-Hermitian.