Hole dynamics and effective hole-hole interaction in a quantum antiferromagnet

By the use of an effective Hamiltonian which takes into account the constraint on the motion of holes in a quantum antiferromagnet, the dynamics of holes is investigated. It is found that there is a quasiparticle band whose width is of order J at the bottom of the hole spectrum. The effective hole-hole interaction mediated by spin fluctuations is derived and the attraction between holes in the d-wave channel is obtained. The results suggest that a d-wave-pairing condensation in a quantum antiferromagnet is very possible.