HMS Mathematical Physics, Heidelberg, December 4, 2009
I will review results, obtained with P. Fendley and L. Huijse, 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 lattice we generically find superfrustration, with ground state entropy that is extensive in the size of system. We establish a theorem relating the ground state degeneracy on the 2D square lattice to specific rhombus tilings of the plane. |