Interaction between two spin polarons in one- and two-dimensional quantum-spin systems

One- (1D) and two-dimensional (2D) quantum-spin systems with additional spins are studied with the exact diagonalization method. The 2D system has a close relation with the high-${\mathit{T}}_{\mathit{c}}$ superconductors, according to the model suggested by one of the authors. Since the transfer energy is taken to be 0 here, the model treated here is reduced to a ‘‘doped’’ Heisenberg antiferromagnet. The creation of spin polarons by the introduction of additional spins is observed in both 1D and 2D systems. Moreover, when two additional spins are doped on different sublattices, the spin state becomes similar to that of the antiferromagnet without additional spins. The interaction between additional spins is obtained as a function of the distance between them and is found to be attractive. It is short ranged in the 1D system while it is long ranged in the 2D system, reflecting the character of the background spin systems.