Phase separation in the t-J model

A detailed understanding of the motion of 'holes' in an antiferromagnet is of fundamental importance for the theory of high-temperature superconductors. It is shown here that, for the t-J model, dilute holes in an antiferromagnet are unstable against phase separation into a hole-rich and a no-hole phase. When the spin-exchange interaction J exceeds a critical value Jc, the hole-rich phase has no electrons. It is proposed that, for J slightly less than Jc, the hole-rich phase is a low-density superfluid of electron pairs. Phase separation in related models is briefly discussed.