# A Study of Topological Quantum Phase Transition and Majorana Localization Length for the Interacting Helical Liquid System

## TL;DR

This paper investigates topological quantum phase transitions and Majorana localization in an interacting helical liquid system, revealing stability differences under attractive and repulsive interactions and edge-dominant excitations.

## Contribution

It provides a comprehensive DMRG study of phase transitions across the entire parameter space, highlighting the role of interactions and chemical potential on Majorana modes.

## Key findings

- Topological phase transition occurs for repulsive interactions.
- Topological phase is more stable under attractive interactions.
- Majorana localization length varies with chemical potential.

## Abstract

We consider a helical spin liquid system which shows majorana fermion modes at the edge. The interaction between the quasiparticles in this system induces phase transition, Majorana-Ising transition. We comply the density matrix renormalization group method to study this phase transition for the entire regime of the parameter space. We observe the presence of topological quantum phase transition for repulsive interaction, however this phase is more stable for the attractive interaction. The length scale dependent study shows many new and important results and we show explicitly that the major contribution to the excitation comes from the edge of the system when the system is in the topological state. We also show the dependence of Majorana localization length for various values of chemical potential.