Doped antiferromagnets in high dimension

The ground-state properties of the $t$-$J$ model on a $d$-dimensional hypercubic lattice are examined in the limit of large $d$. 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 $J>\mathrm{}4t$ and is weakly metallic (and typically superconducting) if $J<\mathrm{}4t$. The resulting phase diagram is qualitatively similar to the one previously derived for $d=2\mathrm{}$ 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 $J/t$, may be either insulating or metallic (i.e., an “electron smectic”).