Deciphering competing interactions of Kitaev-Heisenberg-$\Gamma$ system in clusters: part II -- dynamics of Majorana fermions

TL;DR

This paper systematically studies Majorana fermion dynamics in finite clusters of the Kitaev-Heisenberg-$\Gamma$ model, revealing how external magnetic fields and interactions influence their behavior, with implications for quantum information processing.

Contribution

It provides an exact analysis of Majorana fermion dynamics in finite clusters, highlighting the effects of magnetic fields and interactions on gauge fermion stability and dynamics.

Findings

Magnetic fields significantly alter gauge fermion dynamics.

Gauge fermions exhibit slower dynamics across regimes.

Small clusters of the Kitaev model can test quantum speed limits.

Abstract

We perform a systematic and exact study of Majorana fermion dynamics in the Kitaev-Heisenberg-$\Gamma$ model in a few finite-size clusters increasing in size up to twelve sites. We employ exact Jordan-Wigner transformations to evaluate certain measures of Majorana fermion correlation functions, which effectively capture matter and gauge Majorana fermion dynamics in different parameter regimes. An external magnetic field is shown to produce a profound effect on gauge fermion dynamics. Depending on certain non-zero choices of other non-Kitaev interactions, it can stabilise it to its non-interacting Kitaev limit. For all the parameter regimes, gauge fermions are seen to have slower dynamics, which could help build approximate decoupling schemes for appropriate mean-field theory. The probability of Majorana fermions returning to their original starting site shows that the Kitaev model in small clusters can be used as a test bed for the quantum speed limit.