Power-law spin correlations in a perturbed honeycomb spin model

TL;DR

This paper studies how a weak magnetic field affects the spin correlations in the Kitaev honeycomb model, revealing a power-law decay in spin correlations due to perturbation-induced long-range tails.

Contribution

It demonstrates that a weak magnetic field introduces long-range power-law tails in spin correlations by destroying the model's exact integrability.

Findings

Power-law decay in spin correlations with a $[ ext{max}(t,r)]^{-4}$ tail.

Long-range tails appear in the dynamic spin correlation function due to magnetic perturbation.

The tail's magnitude scales with the square of the magnetic field strength.

Abstract

We consider spin-$\frac{1}{2}$ model on the honeycomb lattice~\cite{Kitaev06} in presence of a weak magnetic field $h_{\alpha }\ll 1$. Such a perturbation destroys exact integrability of the model in terms of gapless fermions and \textit{static} $Z_{2}$ fluxes. We show that it results in appearance of a long-range tail in the irreducible dynamic spin correlation function: $% \left\langle \left\langle s^{z}(t,r)s^{z}(0,0)\right\rangle \right\rangle \propto h_{z}^{2}f(t,r)$, where $f(t,r)\propto \lbrack \max (t,r)]^{-4}$ is proportional to the density polarization function of fermions.