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VOLUME 103 (2016) | ISSUE 2 | PAGE 124
Long-range spin correlations in a honeycomb spin model with magnetic field
We consider spin-1/2 model on the honeycomb lattice (Ann. Phys. 321, 2 (2006)) in presence of weak magnetic field h_{\alpha }\ll J. Such a perturbation treated in the lowest nonvanishing order over hα leads (Phys. Rev. Lett. 106, 067203 (2011)) to a power-law decay of irreducible spin correlations \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,Jr)]^{-4}. In the present Letter we studied the effects of the next order of perturbation in hz and found an additional term of the order hz4 in the correlation function \left\langle\left\langle 
s^{z}(t,r)s^{z}(0,0)\right\rangle\right\rangle which scales as  h_z^4\cos\gamma/r^3 at Jt \ll r, where γ is the polar angle in the 2D plane. We demonstrate that such a contribution can be understood as a result of a perturbation of the effective Majorana Hamiltonian by weak imaginary vector potential A_x \propto i h_z^2.