  We review recent results on lattice models for spin-less fermions with strong
repulsive interactions. A judicious tuning of kinetic and interaction terms
leads to a model possessing supersymmetry. In the 1D case, this model displays
critical behavior described by superconformal field theory. On 2D lattices we
generically find superfrustration, characterized by an extensive ground state
entropy. For certain 2D lattices analytical results on the ground state
structure reveal yet another quantum phase, which we tentatively call
'supertopological'.
