Abstract
We investigate the effect of introducing a boundary inhomogeneity in the transfer matrix of an integrable open quantum spin chain. We find that it is possible to construct a local Hamiltonian, and to have quantum group symmetry. The boundary inhomogeneity has a profound effect on the Bethe ansatz solution.
Highlights
We propose that the eigenvalues of the transfer matrix for general values of n, p and γ0 are given by the following TQ-equation
We have seen that an integrable open quantum spin chain with a boundary inhomogeneity (2.15) can have a local Hamiltonian (2.26)–(2.29), as well as QG symmetry (3.7) that accounts for rich degeneracies in the spectrum
We have focused here on a boundary inhomogeneity whose value is half the period of the R-matrix, and with corresponding staggered bulk inhomogeneities (2.23)
Summary
. .) [22,23,24], which for n = 1 was obtained by Izergin and Korepin [27]; we use the specific form of these R-matrices given in appendix A of [25], with anisotropy parameter η. These R-matrices have the following additional important properties: periodicity. Which for n = 1 was obtained in [31] We emphasize that these K-matrices depend on two boundary parameters p and γ0, which can take the set of discrete values noted in (2.11).
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