Majorana-Hubbard model on the triangular lattice

Majorana fermions are known to arise as emergent particles in certain condensed matter systems. One such realization involves inducing superconductivity on the surface of a 3-dimensional topological insulator, in the presence of a magnetic field. The resulting Abrikosov lattice has a Majorana zero mode (MZM) localized at the core of each vortex. It has been shown that the interaction between MZMs falls off exponentially with the superconducting coherence length. This enables one to write a tight-binding model to describe the system and some of these models have rich phase diagrams that exhibit emergent supersymmetry. Given that in experiments the vortex lattice usually has a triangular geometry, we construct a model for interacting MZMs in this setup. With the interaction strength as a tunable parameter, we study the phase diagram numerically using the density-matrix renormalization group.