The supersymmetric t−J model with quantum group invariance

Integrable Kondo impurities in one-dimensional extended Hubbard models

“…Here ⌳ (1) (u;͕u i ͖) is the eigenvalue of the transfer matrix (1) (u) for the reduced problem, that arises out of the r matrices from the first term in the right-hand side of Eq. ͑58͒, with the reduced boundary K matrices K Ϯ (1) (u) from Eq.…”

“…After some algebra,the reduced transfer matrix (1) (u) may be recognized as that for the inhomogeneous su͑3͒ t-J open chain interacting with the Kondo impurities of arbitrary spins, which has been diagonalized in Ref. 13.…”

“…Noticing the change u→uϩ1 with respect to the original problem, one may check that these boundary K matrices satisfy the reflection equations for the reduced problem. After some algebra,the reduced transfer matrix (1) (u) may be recognized as that for the inhomogeneous su͑3͒ t-J open chain interacting with the Kondo impurities of arbitrary spins, which has been diagonalized in Ref. 13.…”

“…[1][2][3][4][5][6][7][8][9] Recently it has become apparent that for models of open chains it is possible to obtain integrable impurity boundary conditions as operators that need not be expressed in terms of the ͑super͒symmetry of the bulk model. A very important application of this procedure is in the context of Kondo, i.e., spin, impurities in models of correlated electrons.…”

“…A very important application of this procedure is in the context of Kondo, i.e., spin, impurities in models of correlated electrons. For the case of the supersymmetric t-J model boundary spin- 1 2 impurities were introduced in Ref. 10 and the resulting model was solved by means of the coordinate Bethe ansatz method.…”