Luttinger-liquid state of the zigzag double chain

The zigzag double chain is investigated using Lanczos techniques. The weak- coupling limit is similar to that of a ladder system which is known to have a spin gap at half-filling at all coupling strengths. But the half-filled zigzag system is gapless at strong coupling. The question whether a spin ga p occurs upon doping is investigated. It is shown that the doped zigzag cha in is a Luttinger liquid in which the holes repel each other. The criterion is based on exact diagonalization techniques for open shell boundary condi tions. As a further corroboration, the hole-hole and the hole-spin correlat ions are also computed.