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 TMF, 1975, Volume 25, Number 2, Pages 196–212 (Mi tmf4064)

One-particle green s function in the anisotropic Heisenberg model

Yu. G. Rudoi, Yu. A. Tserkovnikov

Abstract: The matrix Green function is studied which is constructed in terms of the Pauli operators and describes the transversal component of the dynamic susceptibility tensor of the anisotropic Heisenberg ferromagnet with spin 1/2 in the transversal and longitudinal external magnetic field. Renormalised magnon spectrum is obtained in the generalised Hartree–Fock approximation (with the damping not taken into account) and phase boundary on the plane “magnetic field – temperature” is evaluated. It is shown that the contribution of the integral term must be taken into account for the fulfillment of the symmetry conditions and the Goldstone–Bogoliubov theorem in the case of the “easy plane” model.

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English version:
Theoretical and Mathematical Physics, 1975, 25:2, 1073–1084

Document Type: Article

Citation: Yu. G. Rudoi, Yu. A. Tserkovnikov, “One-particle green s function in the anisotropic Heisenberg model”, TMF, 25:2 (1975), 196–212; Theoret. and Math. Phys., 25:2 (1975), 1073–1084

Citation in format AMSBIB
\Bibitem{RudTse75} \by Yu.~G.~Rudoi, Yu.~A.~Tserkovnikov \paper One-particle green s function in the anisotropic Heisenberg model \jour TMF \yr 1975 \vol 25 \issue 2 \pages 196--212 \mathnet{http://mi.mathnet.ru/tmf4064} \transl \jour Theoret. and Math. Phys. \yr 1975 \vol 25 \issue 2 \pages 1073--1084 \crossref{https://doi.org/10.1007/BF01028950} 

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This publication is cited in the following articles:
1. V. I. Lymar', Yu. G. Rudoi, “Spectrum and correlation functions of anisotropic Heisenberg antiferromagnet III spin-flop phase in the generalized Hartree–Fock approximation”, Theoret. and Math. Phys., 30:2 (1977), 159–168
2. A. A. Kazakov, “Magnetization of a uniaxial ferromagnet with single-ion and exchange anisotropies in a transverse magnetic field”, Theoret. and Math. Phys., 30:3 (1977), 268–271
3. 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
4. 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
5. 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
6. A. A. Kazakov, “Green's function of a uniaxial ferromagnet with single-ion anisotropy and arbitrary spin in the canted phase”, Theoret. and Math. Phys., 46:3 (1981), 278–280
7. F. P. Onufrieva, “Single-particle Green's function of a ferromagnet with single-ion anisotropy in the presence of a magnetic field of arbitrary direction”, Theoret. and Math. Phys., 54:2 (1983), 196–205
8. 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
9. 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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