  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.
