  We study a Josephson junction in a Kitaev chain with particle-hole symmetric
nearest neighbor interactions. When the phase difference across the junction is
$\pi$, we show analytically that the full spectrum is fourfold degenerate up to
corrections that vanish exponentially in the system size. The Majorana bound
states at the ends of the chain are known to survive interactions. Our result
proves that the same is true for the zero-energy quasiparticle localized at the
junction. We further study finite size corrections numerically, and show how
repulsive interactions lead to stronger end-to-end correlations than in a
noninteracting system with the same bulk gap.
