Renormalization group analysis of phase transitions in the two dimensional Majorana-Hubbard model

Abstract

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 renormalization group methods, and was found to include second order phase transitions. One of these corresponds to spontaneous 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 otherwise. Another second order transition was predicted for repulsive interactions 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 a modified $\epsilon$-expansion, confirming the previous conclusions.

13 pages + 13 pages of appendices

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• Majorana lattices from the quantized Hall limit of a proximitized spin-orbit coupled electron gas
• Supersymmetry in an interacting Majorana model on the kagome lattice
• SO(4) multicriticality of two-dimensional Dirac fermions
• Absence of SO(4) quantum criticality in Dirac semimetals at two-loop order
• Specific heat of 2D interacting Majorana fermions from holography
• Exactly solvable Majorana-Anderson impurity models
• Thermodynamic Behavior of a 4D Nonminimal Maxwell-AdS Black Hole
• Triangular lattice Majorana-Hubbard model: Mean field theory and DMRG on a width-4 torus
• Interacting Majorana fermions in strained nodal superconductors
• Equivalence class of Emergent Single Weyl fermion lattice models in 3 dimensions: gapless superconductors and superfluids versus chiral fermions