Local Quench, Majorana Zero Modes, and Disturbance Propagation in the Ising chain

TL;DR

This paper investigates how local perturbations and Majorana zero modes influence disturbance propagation in the transverse field Ising chain, revealing phase transition signatures and non-ballistic quasiparticle dynamics.

Contribution

It demonstrates that Majorana zero modes enable local detection of phase transitions and significantly alter quasiparticle propagation after local defect removal.

Findings

Local measurements can detect phase transitions via Majorana modes

Majorana modes cause deviations from ballistic quasiparticle propagation

Edge spin dynamics reflect the presence of Majorana zero modes

Abstract

We study the generation and propagation of local perturbations in a quantum many-body spin system. In particular, we study the Ising model in transverse field in the presence of a local field defect at one edge. This system possesses a rich phase diagram with different regions characterized by the presence of one or two Majorana zero modes. We show that their localized character {\it i}) enables a characterization of the Ising phase transition through a local-only measurement performed on the edge spin, and {\it ii}) strongly affects the propagation of quasiparticles emitted after the sudden removal of the defect, so that the dynamics of the local magnetization show clear deviations from a ballistic behavior in presence of the Majorana fermions.