Long-range spin correlations in a honeycomb spin model with a magnetic field
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We consider the spin-1/2 model on the honeycomb lattice [A. Kitaev, Ann. Phys. 321, 2 (2006)] in the presence of a weak magnetic field h α ≪ J. Such a perturbation treated in the lowest nonvanishing order over h α leads [K.S. Tikhonov, M.V. Feigel’man, and A.Yu. Kitaev, Phys. Rev. Lett. 106, 067203 (2011)] to a powerlaw decay of irreducible spin correlations 《s z (t, r)s z (0, 0)》 ∝ h z 2 f(t, r), where f(t, r) ∝ [max(t, Jr)]–4. We have studied the effects of the next order of perturbation in h z and found an additional term of the order h z 4 in the correlation function 《s z (t, r)s z (0, 0)》 which scales as h z 4 cosγ/r 3 at Jt≪ 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 the weak imaginary vector potential A x ∝ i h z 2 .
KeywordsJETP Letter Spin Operator Spin Correlation Weak Magnetic Field Honeycomb Lattice
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