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 TMF, 1974, Volume 19, Number 2, Pages 252–268 (Mi tmf3583)

Single-particle Green's function in an anisotropic Heisenberg model. III. Spectrum and damping for anisotropy of the easy plane type

Yu. G. Rudoi, Yu. A. Tserkovnikov

Abstract: A study is made of the matrix Green's function constructed from Pauli operators similar to the one used in the theory of superfluidtty and superconductivity. The poles of the dynamical susceptibility and a renormalized spectrum of Bogolyubov-type magnons are found. General expressions are obtained for the normal and anomalous stngle-particle correlation functions and also an equation for the magnetization that generalizes Tyablikov theory. A canonical $u-v$-transformation is applied to the quasi-Bose operators in order to calculate the contribution of the integral term of second order to the energy shift and damping of magnons at low temperatures.

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English version:
Theoretical and Mathematical Physics, 1974, 19:2, 491–503

Citation: Yu. G. Rudoi, Yu. A. Tserkovnikov, “Single-particle Green's function in an anisotropic Heisenberg model. III. Spectrum and damping for anisotropy of the easy plane type”, TMF, 19:2 (1974), 252–268; Theoret. and Math. Phys., 19:2 (1974), 491–503

Citation in format AMSBIB
\Bibitem{RudTse74} \by Yu.~G.~Rudoi, Yu.~A.~Tserkovnikov \paper Single-particle Green's function in an~anisotropic Heisenberg model. III.~Spectrum and damping for anisotropy of the easy plane type \jour TMF \yr 1974 \vol 19 \issue 2 \pages 252--268 \mathnet{http://mi.mathnet.ru/tmf3583} \transl \jour Theoret. and Math. Phys. \yr 1974 \vol 19 \issue 2 \pages 491--503 \crossref{https://doi.org/10.1007/BF01035950} 

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This publication is cited in the following articles:
1. V. I. Lymar', Yu. G. Rudoi, “Spectrum and correlation functions of an anisotropic Heisenberg antiferromagnet I. Antiferromagnetic phase in the generalized Hartree-Fock approximation”, Theoret. and Math. Phys., 21:1 (1974), 990–1002
2. V. I. Lymar', Yu. G. Rudoi, “Spectrum and correlation functions of an anisotropic heisenberg antiferromagnet. II. Paramagnetic phase in the generalized Hartree–Fock approximation”, Theoret. and Math. Phys., 24:3 (1975), 912–917
3. Yu. G. Rudoi, Yu. A. Tserkovnikov, “One-particle green s function in the anisotropic Heisenberg model”, Theoret. and Math. Phys., 25:2 (1975), 1073–1084
4. R. R. Nigmatullin, “Exact structure of equations for the longitudinal correlation function in the anisotropic Heisenberg ferromagnet”, Theoret. and Math. Phys., 28:3 (1976), 869–877
5. E. V. Kuz'min, S. G. Ovchinnikov, “Electron correlations in a Hubbard antiferromagnetic semiconductor. Weak coupling”, Theoret. and Math. Phys., 31:3 (1977), 523–531
6. V. I. Lymar', Yu. G. Rudoi, “Spectrum and correlation functions of an anisotropic heisenberg antiferromagnet. IV. Model of easy plane type with allowance for Dzyaloshinskii interaction”, Theoret. and Math. Phys., 34:2 (1978), 137–147
7. Yu. G. Rudoi, “Tensor of the inhomogeneous dynamic susceptibility of an anisotropic Heisenberg ferromagnet and Bogolyubov inequalities. I. Single-particle matrix Green's function and transverse components of the susceptibility tensor”, Theoret. and Math. Phys., 38:1 (1979), 68–78
8. V. V. Val'kov, S. G. Ovchinnikov, “Hubbard operators and spin-wave theory of Heisenberg magnets with arbitrary spin”, Theoret. and Math. Phys., 50:3 (1982), 306–313
9. V. V. Val'kov, “Unitary transformations of the group $U(N)$ and diagonalization of multilevel Hamiltonians”, Theoret. and Math. Phys., 76:1 (1988), 766–772
10. Yu. G. Rudoy, “The Bogoliubov–Tyablikov Green's function method in the quantum theory of magnetism”, Theoret. and Math. Phys., 168:3 (2011), 1318–1329
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