Fusion procedure for open chains

Bethe ansatz solution of the openXXspin chain with non-diagonal boundary terms

“…(This approach does not completely circumvent the problem of not having a reference state, since the eigenvectors are not determined.) We obtain the inversion identity using the open-chain fusion formula [16] together with the remarkable fact that, for the open XX spin chain/ 6-vertex free-Fermion model, the fused transfer matrix is proportional to the identity matrix. A similar strategy has recently been used [13] to solve the open 8-vertex free-Fermion [17] model, which corresponds to the case of N = 1 supersymmetry.…”

Exact spectrum of the spin-s Heisenberg chain with generic non-diagonal boundaries

“…Having defined the fused-R matrices, one can analogously construct the fused-K matrices by using the methods developed in [69,74,75] as follows. The fused K − matrices (e.g the spin-j K − matrix) is given by…”

“…}, i.e., each of the N quantum spaces is described by a spin S ((2s + 1)-dimensional). The fused transfer matrices {t (j,s) (u)} given by (2.23) obey the following fusion hierarchy relation [52,69,74,75] …”

Nested off-diagonal Bethe ansatz and exact solutions of the su(n) spin chain with generic integrable boundaries

“…In this case, we need to use the fusion techniques both for R-matrices [65][66][67][68][69] and for K-matrices [75,76]. We only consider the antisymmetric fusion procedure which leads to the desired operator identities to determine the spectrum of the transfer matrix t(u) given by (3.5).…”

“…We only consider the antisymmetric fusion procedure which leads to the desired operator identities to determine the spectrum of the transfer matrix t(u) given by (3.5). Following [75,76], let us introduce the fused K-matrices and double-row monodromy matrices by the following recursive relations…”