Phase separation in the large-spin t-J model

We investigate the phase diagram of the two-dimensional t-J model using a recently developed technique that allows one to solve the mean-field model Hamiltonian with a variational calculation. The accuracy of our estimate is controlled by means of a small parameter 1/q, analogous to the inverse spin magnitude 1/s employed in studying quantum spin systems. The mathematical aspects of the method and its connection with other large-spin approaches are discussed in detail. In the large-q limit the problem of strongly correlated electron systems turns into the minimization of a total-energy functional. We have performed this optimization numerically on a finite but large L x L lattice. For a single hole the static small-polaron solution is stable except for small values Of J, where polarons of increasing sizes have lower energy. At finite doping we recover phase separation above a critical J and for any electron density, showing that the Emery et al. picture represents the semiclassical behavior of the t-J model. Quantum fluctuations are expected to be very important, especially in the small-J-small-doping region, where Phase separation may also be suppressed.