Majorana-Hubbard model on the square lattice

We study a tight-binding model of interactingMajorana (Hermitian) modes on a square lattice. The model may have an experimental realization in a superconducting-film-topological-insulator heterostructure in a magnetic field. We find a rich phase diagram, as a function of interaction strength, including an emergent superfluid phase with spontaneous breaking of an emergent U(1) symmetry, separated by a supersymmetric transition from a gapless normal phase.