A Renormalization Group Study of Interacting Helical Liquid : Physics of Majorana Fermion

TL;DR

This paper investigates the effects of interactions on Majorana fermions in one-dimensional helical liquids using renormalization group analysis, revealing phase transitions and conditions for Majorana mode emergence.

Contribution

It provides the RG equations for strongly interacting helical liquids and analyzes topological phase transitions, including the impact of interactions and umklapp scattering.

Findings

Majorana-Ising transition is exactly solvable in non-interacting case

Interactions eliminate the exactly solvable line, complicating phase analysis

Conditions for Majorana fermion modes depend on RG flow and umklapp scattering

Abstract

The physics of Majorana fermion occurs at the edge and interface of many one-dimensional quantum many body system with gapped excitation spectrum. We present the renormalization group equations for strongly interacting helical liquid. We present the results of both Majorana- Ising topological quantum phase transition and also Berezinskii-Kosterlitz-Thouless topological phase transition. We show that the Majorana-Ising topological quantum phase transition for non-interacting case is an exactly solvable line but in presence of interaction the system has no exactly solvable line. We study the effect of umklapp scattering on the renormalization group flow diagrams and also the condition for the appearence of Majorana fermion modes.