We present a microscopic model of interacting fermions where the ground
state degeneracy is topologically protected. The model is based on a
double-wire setup with local interactions in a particle number
conserving setting. A compelling property of this model is the exact
solvability for its ground states and low energy excitations. We
demonstrate the appearance of topologically protected edge states and
derive their braiding properties on a microscopic level. We find the
non-abelian statistics of Ising anyons, which can be interpreted as
Majorana-like edge states.