  We have investigated the effects of long-range Coulomb interaction on the
topological superconducting phase in a quasi-one dimensional semiconductor
wire, proximity coupled to a s-wave using the exact diagonalization approach.
We find that in accordance with previous studies the addition of Coulomb
interaction results in an enlargement of the region of parameter values where
topological superconductivity can be observed. However, we also find that
although the interaction decreases the bulk gap for values of the magnetic
field close to the phase transition point, for moderate magnetic fields away
from the transition point, the interaction actually enhances the bulk gap which
can be important for observation of topological superconductivity in this
system.
