# Disorder and interaction in chiral chains: Majoranas vs complex fermions

## TL;DR

This paper investigates how interactions and disorder differently affect chains of Majorana versus complex fermions, revealing that interactions destabilize Majorana chains leading to localization, unlike complex fermion chains which remain at the critical point.

## Contribution

It demonstrates that interactions cause Majorana chains to undergo symmetry breaking and localization, contrasting with the stability of complex fermion chains at the non-interacting fixed point.

## Key findings

- Majorana chains localize with repulsive interactions
- Complex fermion chains remain at the non-interacting fixed point
- Interaction operators destabilize the Majorana critical state

## Abstract

We study the low-energy physics of a chain of Majorana fermions in the presence of interaction and disorder, emphasizing the difference between Majoranas and conventional (complex) fermions. While in the non-interacting limit both models are equivalent (in particular, belong to the same symmetry class BDI and flow towards the same infinite-randomness critical fixed point), their behavior differs drastically once interaction is added. Our density-matrix renormalization group calculations show that the complex-fermion chain remains at the non-interacting fixed point. On the other hand, the Majorana fermion chain experiences a spontaneous symmetry breaking and localizes for repulsive interaction. To explain the instability of the critical Majorana chain with respect to a combined effect of interaction and disorder, we consider interaction as perturbation to the infinite-randomness fixed point and calculate numerically two-wavefunction correlation functions that enter interaction matrix elements. The numerical results supported by analytical arguments exhibit a rich structure of critical eigenstate correlations. This allows us to identify a relevant interaction operator that drives the Majorana chain away from the infinite randomness fixed point. For the case of complex fermions, the interaction is irrelevant.