Finite compressibility in the low-doping region of the two-dimensional t-J model

We reexamine the important issue of charge fluctuations in the two-dimensional t-J model by using an improved variational method based on a wave function that contains both antiferromagnetic and d-wave superconducting order parameters. In particular, we generalize the wave function introduced some time ago by Bouchaud, Georges, and Lhuillier [J. Phys. (Paris) 49, 553 (1988)] by considering also a long-range spin-spin Jastrow factor, in order to correctly reproduce the small-q behavior of the spin fluctuations. We mainly focus our attention on the physically relevant region J/t similar to 0.4 and find that, contrary to a previous variational ansatz, this state is stable against phase separation for small hole doping. Moreover, by performing projection Monte Carlo methods based on the so-called fixed-node approach, we obtain clear evidence that the t-J model does not phase separate for J/t less than or similar to 0.7 and that the compressibility remains finite close to the antiferromagnetic insulating state.