Disorder effects in the $\mathbb{Z}_{3}$ Fock parafermion chain

TL;DR

This paper investigates how disorder affects a one-dimensional $ ext{Z}_3$ Fock parafermion chain, revealing the presence of many-body localization driven by particle statistics, using exact diagonalization and tensor network methods.

Contribution

It demonstrates that a quadratic $ ext{Z}_3$ parafermion model exhibits many-body localization without Anderson localization, highlighting the role of particle statistics.

Findings

Identification of ergodic and localized phases in the model

Distinction between Anderson and many-body localization effects

Evidence that nontrivial statistics induce many-body localization

Abstract

We study the effects of disorder in a one-dimensional model of $\mathbb{Z}_{3}$ Fock parafermions which can be viewed as a generalization of the prototypical Kitaev chain. Exact diagonalization is employed to determine level statistics, participation ratios, and the dynamics of domain walls. This allows us to identify ergodic as well as finite-size localized phases. In order to distinguish Anderson from many-body localization, we calculate the time evolution of the entanglement entropy in random initial states using tensor networks. We demonstrate that a purely quadratic parafermion model does not feature Anderson but many-body localization due to the nontrivial statistics of the particles.