Long-range spin correlations in a honeycomb spin model with magnetic field

Abstract

We consider spin-$\frac{1}{2}$ model on the honeycomb lattice in the presence of weak magnetic field $h\ll J$. Such a perturbation treated in the second order over $h$ leads to the power-law decay of irreducible spin correlation function $S(\mathbf{r},t)=⟨⟨s_r^z(t)s_0^z(0)⟩⟩\propto h_z^{2}f(t,\mathbf{r})$, where $f(t,\mathbf{r})\propto [\max (t,Jr){]}^{-4}$ is an oscillating function of $\mathbf{r}$, with a wavelength equal to 3 lattice constants. In the present Letter we sum main terms in all orders of the perturbation theory for the correlation function $S(\mathbf{r},t)$ in the limit of large $r,t$. Our results can be understood in terms of the effective low-energy Hamiltonian written in terms of Majorana fermions, which in the presence of magnetic field acquire vector potential $A_x\propto h_z^2$. Correspondingly, the wave vector of the oscillations in $S(\mathbf{r},t)$ changes according to $\delta k\propto h_z^2$. We also compute the dynamic structure factor $S(\mathbf{p},\omega )$; in the vicinity of ${\mathbf{p}}_K$ corresponding to the inter-conical points excitations it reads as $S(\mathbf{p},\omega )-S({\mathbf{p}}_K,\omega )\propto \sqrt{{\omega }^2-3J^2(\mathbf{p}-{\mathbf{p}}_K{)}^2}$.

8 pages, 2 figures. Extended and corrected version of the paper published in JETP Lett. v.103, p.117 (2016)

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• Exact results for spin dynamics and fractionization in the Kitaev Model
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