  Majorana modes can arise as zero energy bound states in a variety of solid
state systems. A two-dimensional phase supporting these quasiparticles, for
instance, emerges on the surface of a topological superconductor with the zero
modes localized at the cores of vortices. At low energies, such a setup can be
modeled by Majorana modes that interact with each other on the Abrikosov
lattice. In experiments, the lattice is usually triangular. Motivated by the
practical relevance, we explore the phase diagram of this Hubbard-like Majorana
model using a combination of mean field theory and numerical simulation of thin
torus geometries through the density matrix renormalization group algorithm.
Our analysis indicates that attractive interactions between Majoranas can drive
a phase transition in an otherwise gapped topological state.
