Exact Ground State and Finite Size Scaling in a Supersymmetric Lattice Model

We study a model of strongly correlated fermions in one dimension with extended N=2 supersymmetry. The model is related to the spin $S=1/2$ XXZ Heisenberg chain at anisotropy $\Delta=-1/2$ with a real magnetic field on the boundary. We exploit the combinatorial properties of the ground state to determine its exact wave function on finite lattices with up to 30 sites. We compute several correlation functions of the fermionic and spin fields. We discuss the continuum limit by constructing lattice observables with well defined finite size scaling behavior. For the fermionic model with periodic boundary conditions we give the emptiness formation probability in closed form.