Doped antiferromagnets in the weak-hopping limit

We study the phase diagram of the two-dimensional t-J-V model of holes in a two-dimensional antiferromagnet in the J≫t limit. Here t is the hole hopping parameter, J is the exchange coupling between nearest-neighbor spins, and V is the nearest-neighbor electron-electron repulsion. We also include the possibility of Heisenberg-Ising anisotropy, ${\mathit{J}}_{\mathrm{\perp }}$≠${\mathit{J}}_{\mathit{z}}$. We obtain a complete description for ${\mathit{J}}_{\mathrm{\perp }}$≪${\mathit{J}}_{\mathit{z}}$ and approximate results for ${\mathit{J}}_{\mathrm{\perp }}$=${\mathit{J}}_{\mathit{z}}$. There is no region of the zero-temperature phase diagram that supports a dilute gas of holes in an antiferromagnet. Rather, the system always phase separates into hole-rich and no-hole phases, a result we believe to be more general than the model we have considered. We find various hole-crystal phases and, at high hole density, we find a ‘‘Fermi-liquid’’ phase and at least two superfluid phases, one with a charge 2e and one with a charge 4e order parameter.