Anomalous Quantum Information Scrambling for $\mathbb{Z}_3$ Parafermion Chains

TL;DR

This paper investigates quantum information scrambling in $ ext{Z}_3$ parafermion chains using generalized OTOCs, revealing unique symmetric and asymmetric light cone behaviors and evidence of strong zero modes at infinite temperature.

Contribution

It introduces an efficient matrix product operator method to compute OTOCs in parafermion chains and uncovers novel scrambling dynamics and boundary effects.

Findings

Parafermion chains exhibit both symmetric and asymmetric light cones.

Strong zero modes are evidenced at infinite temperature.

Deformed light cone structure with boundary peaks in topological regimes.

Abstract

Parafermions are exotic quasiparticles with non-Abelian fractional statistics that could be exploited to realize universal topological quantum computing. Here, we study the scrambling of quantum information in one-dimensional parafermionic chains, with a focus on $\mathbb{Z}_3$ parafermions in particular. We use the generalized out-of-time-ordered correlators (OTOCs) as a measure of the information scrambling and introduce an efficient method based on matrix product operators to compute them. With this method, we compute the OTOCs for $\mathbb{Z}_3$ parafermions chains up to $200$ sites for the entire early growth region. We find that, in stark contrast to the dynamics of conventional fermions or bosons, the information scrambling light cones for parafermions can be both symmetric and asymmetric, even for inversion-invariant Hamiltonians involving only hopping terms. In addition, we find a deformed light cone structure with a sharp peak at the boundary of the parafermion chains in the topological regime, which gives a unambiguous evidence of the strong zero modes at infinite temperature.