A self-consistent analytic theory of the spin bipolaron in the t-J model

The spin bipolaron in the t-J model, i.e., two holes interacting with an an tiferromagnetic spin background, is treated by an extension of the self-con sistent Born approximation (SCBA), which has proved to be very accurate in the single-hole (spin polaron) problem. One of the main ingredients of our approach is the exact form of the bipolaron eigenstates in terms of a compl ete set of two-hole basis vectors. This enables us to eliminate the hole op erators and to obtain the eigenvalue problem solely in terms of the boson ( magnon) operators. The eigenvalue equation is then solved by a procedure si milar to Reiter's construction of the single-polaron wave function in the S CBA. As in the latter case, the eigenvalue problem comprises a hierarchy of infinitely many coupled equations. These are brought into a soluble form b y means of the SCBA and an additional decoupling approximation, whereupon t he eigenvalue problem reduces to a linear integral equation involving the b ipolaron self-energy. The numerical solutions of the integral equation are in quantitative agreement with the results of previous numerical studies of the problem. The d-wave bound state is found to have the lowest energy wit h a critical value J\t\(c) approximate to 0.4. In contrast to recent claims , we find no indication for a crossover between the d-wave and p-wave bound states.