Renormalization group analysis of phase transitions in the two dimensional Majorana-Hubbard model
A lattice of interacting Majorana modes can occur in a superconducting film on a topological insulator in a magnetic field. The phase diagram as a function of interaction strength for the square lattice was analyzed recently using a combination of mean field theory and field theory and was found to include second order phase transitions. One of these corresponds to sponta- neous breaking of an emergent U(1) symmetry, for attractive interactions.
Despite the fact that the U(1) symmetry is not exact, this transition was claimed to be in a supersymmetric universality class when time reversal symmetry is present and in the conventional XY universality class when it is absent. Another second order transition was predicted for repulsive in- teractions with time reversal symmetry to be in the same universality class as the transition occurring in the Gross-Neveu model, despite the fact that the U(1) symmetry is not exact in the Majorana model. We analyze these phase transitions using the -expansion, and show that the emergent U(1) symmetry is not broken at either critical point. We also show that for a sufficiently weak fermion mass, supersymmetry remains at the transition for attractive interactions. When the fermion mass is large, the conventional XY transition is obtained.