Phase separation in t − J ladders

The phase separation boundary of isotropic t-J ladders is analyzed using density matrix renormalization group techniques. The complete boundary to phase separation as a function of J/t and doping is determined for a chain and for ladders with two, three, and four legs. Six-chain ladders have been analyzed at low hole doping. We use a direct approach in which the phase separation boundary is determined by measuring the hole density in the part of the system which contains both electrons and holes. In addition, we examine the binding energy of multihole clusters. An extrapolation in the number of legs suggests that the lowest J/t for phase separation to occur in the two-dimensional t-J model is J/t;1.