2 On the theory of magnetic impurities in integrable correlated electron chains

In a recent preprint [1] Ge et al. reply to our recent response [2] to some concerns raised in [3]. Several obvious remarks are necessary to clarify the situation, because the authors of [1] certainly misunderstand (or misinterpret) some of our statements. 1. In [3] and in [4] the authors imply that integrable magnetic impurities cannot exist in closed t−J and Hubbard chains (cf. P. 795 of [4] and P. 8544 of [3]). It turns out that in [1] they admit that integrable magnetic impurities can exist in exactly solvable closed correlated electron chains. 2. The approach (i) in our answer [2] has been named the " quantum inverse scattering method " (also known as the algebraic Bethe ansatz cf. [5]) long before our work on impurities in correlated electron systems, see, e.g., [6]. This standard definition has been used in our reply [2]. The approach (ii) in our reply [2] is known as the " graded quantum inverse scattering method " [7]. Does the strong emphasis in [1] on the difference between the coordinate Bethe ansatz and the quantum inverse scattering method imply that the authors of [1] believe that those two methods could yield different answers? We are not aware of any such contradictions between the two methods. 3. In [2] we pointed out that the impurity matrix changes the commutation relations in the spin sector (see below). This is absolutely correct, keeping in mind that two parameters, θ and S, which distinguish the impurity site from other sites of the chain are nonzero (note that the impurity scattering matrix used in our papers [8, 9, 10] mixes the states with S and S + 1 2 ; this hybridization is sometimes misunderstood). 4. The magnetic impurities we studied in our papers have an essentially different structure than those of [11]; hence, it is no wonder that the solutions do not coincide with ours. Ref. [12] considers the supersymmetric t−J model with a different grading than the 1