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 -expansion, confirming the previous conclusions.

Phase diagrams of SO($N$) Majorana-Hubbard models: Dimerization, internal symmetry breaking, and fluctuation-induced first-order transitions

“…Importantly, the width of the Majorana bands can be tuned by a gate voltage in these systems, allowing one to access the regime of strong interactions between Majorana fermions even with weak underlying electron-electron interactions [6]. Besides applications in topological quantum computing [7], two-dimensional Majorana fermion systems have therefore received interest as tunable platforms to investigate effects of strong interactions, spontaneous symmetry breaking, and quantum phase transitions [8][9][10][11][12].…”

Quantum liquid crystals in the finite-field K$Γ$ model for $α$-RuCl$_3$

“…In this Letter, we study a phase diagram of the finitefield KΓ model using the third-order perturbation. The effective model is an interacting Majorana model with four-body and six-body interactions [32][33][34][35][36][37][38][39][40][41]. Based on the mean-field solution and the exact diagonalization, we find the phase diagram is rich enough to predict various exotic spin liquids like NKSL and KKSL.…”

Topological Nematic Phase Transition in Kitaev Magnets Under Applied Magnetic Fields

“…Our proposal paves the way for materializing the toric code phase, which can be utilized for realizing fault-tolerant quantum computation, in real magnetic materials. Although effects of interactions between Majorana fermions have been extensively studied before for Kitaev magnets as well as topological superconductors [8,[32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49], physics arising from Majorana interactions in the nonperturbative regime has not yet been fully understood. By combining the mean-field analysis and the numerical exact diagonalization method, we elucidate that the four-body interactions can induce nematic-type Majorana bond ordered phase which is a gapped QSL with zero Chern number, i.e.…”