Exact results for a Kondo problem in a one-dimensional t-J model

We propose an integrable Kondo problem in a one-dimensional t-J model. With the open boundary condition of the wave functions at the impurity sites, the model can be exactly solved via Bethe ansatz for a set of J(L,R) (Kondo coupling constants) and V-L,V-R (impurity potentials) parametrized by a single parameter c. The integrable value of J(L,R) runs from negative infinity to positive infinity, which allows us to study both the ferromagnetic Kondo problem and the antiferromagnetic Kondo problem in a strongly correlated electron system. Generally, there is a residual entropy for the ground state, which indicates a typical non-Fermi liquid behavior.