Transition between hole pairs and four-hole clusters in four-leg t-J ladders -: art. no. 205109

Holes weakly doped into a four-leg t-J ladder bind in pairs. At dopings exceeding a critical doping of delta(c)similar or equal to1/8 four-hole clusters are observed to form in density-matrix renormalization-group calculations. The symmetry of the ground-state wave function does not change and we are able to reproduce this behavior qualitatively with an effective bosonic model in which the four-leg ladder is represented as two coupled two-leg ladders and hole pairs are mapped on hard-core bosons moving along and between these ladders. At lower dopings, delta<delta(c), a one-dimensional bosonic representation for hole pairs works and allows us to calculate accurately the Luttinger liquid parameter K-rho that takes the universal value K-rho=1 as half-filling is approached.