Doped antiferromagnets in high dimension

The ground-state properties of the (Formula presented)-(Formula presented) model on a (Formula presented)-dimensional hypercubic lattice are examined in the limit of large (Formula presented). It is found that the undoped system is an ordered antiferromagnet, and that the doped system phase separates into a hole-free antiferromagnetic phase and a hole-rich phase. The latter is electron free if (Formula presented) and is weakly metallic (and typically superconducting) if (Formula presented). The resulting phase diagram is qualitatively similar to the one previously derived for (Formula presented) by a combination of analytic and numerical methods. Domain-wall (or stripe) phases form in the presence of weak Coulomb interactions, with periodicity determined by the hole concentration and the relative strength of the exchange and Coulomb interactions. These phases reflect the properties of the hole-rich phase in the absence of Coulomb interactions, and, depending on the value of (Formula presented), may be either insulating or metallic (i.e., an “electron smectic”).