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.

arXiv comment13 pages + 13 pages of appendices

References in corpus (27)

• New directions in the pursuit of Majorana fermions in solid state systems
• Search for Majorana fermions in superconductors
• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Interactions and phase transitions on graphene's honeycomb lattice
• Naturalness Versus Supersymmetric Non-renormalization Theorems
• TikZ-Feynman: Feynman diagrams with TikZ
• Theory of interacting electrons on the honeycomb lattice
• Emergent Space-time Supersymmetry at the Boundary of a Topological Phase
• Relativistic Mott criticality in graphene
• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• Emergent Supersymmetry from Strongly Interacting Majorana Zero Modes
• The N-component Ginzburg-Landau Hamiltonian with cubic anisotropy: a six-loop study
• Emergence of supersymmetry at a critical point of a lattice model
• Phase Diagram of the Interacting Majorana Chain Model
• Bootstrapping the Three-Dimensional Supersymmetric Ising Model
• Emergence of supersymmetry on the surface of three dimensional topological insulators
• Strongly interacting Majorana fermions
• Emergence of U(1) symmetry in the 3D XY model with Zq anisotropy
• Ordered phase and scaling in $Z_n$ models and the three-state antiferromagnetic Potts model in three dimensions
• Statistical translation invariance protects a topological insulator from interactions
• Electronic transport in an array of quasi-particles in the nu=5/2 non-abelian quantum Hall state
• Superconducting quantum criticality of topological surface states at three loops
• Majorana-Hubbard model on the square lattice
• Scaling dimensions in QED${}_3$ from the $\epsilon$-expansion
• Majorana-Hubbard model on the honeycomb lattice
• Yukawa CFTs and Emergent Supersymmetry
• Majorana stripe order on the surface of a three-dimensional topological insulator

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• Majorana lattices from the quantized Hall limit of a proximitized spin-orbit coupled electron gas
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• 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
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• Thermodynamic Behavior of a 4D Nonminimal Maxwell-AdS Black Hole
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