Holon pairing instability based on the Bethe-Salpeter equation obtained from the t-J Hamiltonians of both U(1) and SU(2) slave-boson symmetries

A Bethe-Salpeter equation is obtained by using of the t-J Hamiltonians that satisfy the U(1) and the SU(2) slave-boson symmetries, respectively. Holon-holon scattering channels in the Bethe-Salpeter equation are judiciously examined at a critical temperature to study the instability of the normal state against holon pairing. From the present study of the holon pairing instability, an arch-shaped bose condensation line is revealed in agreement with the observation for high-Tc cuprates over a range of hole doping concentration.