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

We revisit 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 the antiferromagnetic and the d-wave superconducting order parameters. In particular, we generalize the wave function introduced some time ago by J.P. Bouchaud, A. Georges, and C. Lhuillier [J. de Physique {\bf 49}, 553 (1988)] by considering also a {\it 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∼0.4 and find that, contrary to 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 a clear evidence that the t−J model does not phase separate for J/t≲0.7 and that the compressibility remains finite close to the antiferromagnetic insulating state.