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 TMF, 1973, Volume 15, Number 3, Pages 388–406 (Mi tmf3679)

Single-particle Green's function in the anisotropic Heisenberg model II. Allowance for higher correlation functions

Yu. G. Rudoi, Yu. A. Tserkovnikov

Abstract: The spectrum and damping of magnons is found on the basis of a self-consistent allowance for the dynamics and kinematics of the Pauli operators in an integral term of second order in the interaction. A generalized Tyablikov equation is obtained for the magnetization, this being applicable in the whole range of temperatures and fields and nat containing a term $T_3$ at small $T$. It is shown that the rigorous Dyson theory corresponds exactly to the approximation of the two-particle $T$ scattering matrix of the magnons (without allowance for bound states), so that the nonunitary Dyson–Maleev transformation to Bose operators becomes superfluous. Dyson's equations are generalized to the anisotropic case and a correction is found to the gap in the magnon spectrum.

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English version:
Theoretical and Mathematical Physics, 1973, 15:3, 600–613

Document Type: Article

Citation: Yu. G. Rudoi, Yu. A. Tserkovnikov, “Single-particle Green's function in the anisotropic Heisenberg model II. Allowance for higher correlation functions”, TMF, 15:3 (1973), 388–406; Theoret. and Math. Phys., 15:3 (1973), 600–613

Citation in format AMSBIB
\Bibitem{RudTse73}
\by Yu.~G.~Rudoi, Yu.~A.~Tserkovnikov
\paper Single-particle Green's function in the anisotropic Heisenberg model~II. Allowance for higher correlation functions
\jour TMF
\yr 1973
\vol 15
\issue 3
\pages 388--406
\mathnet{http://mi.mathnet.ru/tmf3679}
\transl
\jour Theoret. and Math. Phys.
\yr 1973
\vol 15
\issue 3
\pages 600--613
\crossref{https://doi.org/10.1007/BF01094568}

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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. 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”, Theoret. and Math. Phys., 19:2 (1974), 491–503
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. Yu. A. Tserkovnikov, “Calculation of correlation functions in the case of degeneracy of the state of statistical equilibrium”, Theoret. and Math. Phys., 23:2 (1975), 467–478
5. Yu. A. Tserkovnikov, “Calculation of the correlation functions of a nonideal Bose gas by the method of collective variables”, Theoret. and Math. Phys., 26:1 (1976), 50–61
6. Yu. G. Rudoi, “Quasicollective spin waves in the paramagnetic region of an anisotropic Heisenberg ferromagnet”, Theoret. and Math. Phys., 26:3 (1976), 263–269
7. 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
8. 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
9. Yu. A. Tserkovnikov, “Construction of the correlation functions of the Heisenberg ferromagnet in the ferromagnetic and paramagnetic regions”, Theoret. and Math. Phys., 40:2 (1979), 726–738
10. 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
11. 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
12. N. M. Plakida, “The two-time Green's function and the diagram technique”, Theoret. and Math. Phys., 168:3 (2011), 1303–1317
13. 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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