  We consider a chain of spinful fermions with nearest neighbor hopping in the
presence of a $XY$ antiferromagnetic interaction. The $XY$ term is mapped onto
a Kitaev chain at half-filling such that displays a bosonic zero mode
topologically protected and long-range order. As the strength of the hopping
amplitude is changed, the system undergoes a quantum phase transition from the
topological non-trivial to the trivial phase. We apply the finite-size scaling
method to determinate the phase diagram of the model.
