Slow holes in the triangular Ising antiferromagnet

We consider the problem of the doped Ising antiferromagnet on the frustrate d triangular lattice in the limit where the hole kinetic energy is much sma ller than the Ising exchange. For a single hole we prove a "frustrated Naga oka theorem" showing that the ground state is magnetized and breaks transla tional symmetry, in contrast to the parent insulating state that is unmagne tized and spatially homogeneous. The extension of this physics to finite do pings depends on the strength of a density-density coupling that is inevita bly present-we find either phase separation of the holes, or a superconduct ing state that is also magnetized and breaks translational symmetry in a fe at of spatial self-organization. Finally, we derive an effective interactio n between dilute holes at temperatures in excess of the hopping and find an oscillatory, long-ranged form reflective of the correlations in the underl ying classical magnet which presages the breaking of translational symmetry at zero temperature.