## Abstract

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} ∝ ih_{z} ^{2}.

Original language | English |
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Pages (from-to) | 117-121 |

Number of pages | 5 |

Journal | JETP Letters |

Volume | 103 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Jan 2016 |

Externally published | Yes |