Results for a doped three-leg $t$-$J$ ladder obtained using the density-matrix renormalization group are reported. At low hole doping, the holes form a dilute gas with a uniform density. The momentum occupation of the odd band shows a sharp decrease at a large value of $k_F$ similar to the behavior of a lightly doped $t$-$J$ chain, while the even modes appear gapped. The spin-spin correlations decay as a power law consistent with the absence of a spin gap, but the pair-field correlations are negligible. At larger doping we find evidence for a spin gap and as $x$ increases further we find three-hole diagonal domain walls. In this regime there are significant pair-field correlations and the internal pair orbital has $d_{x^2-y^2}$-like symmetry.

• Received 25 June 1997

DOI:https://doi.org/10.1103/PhysRevB.57.3031