Abstract:
It is shown that a number of first-order theories that are widely used in the quantum theory
of a uniaxially anisotropic Heisenberg ferromagnet with spin $1/2$ can be obtained in a simple
and unified manner on the basis of a formally exact solution of the equation of motion
for the single-magnon Green's function. All these theories give a renormalization of the
energy of Btoch magnons without allowance for damping and differ by the degree to which
the dynamic and the kinematic interaction are allowed for in an estimate of the spectrum
in the generalized Hartree–Fok approximation.
Citation:
Yu. G. Rudoi, Yu. A. Tserkovnikov, “Single-particle Green's function in an anisotropic Heisenberg model”, TMF, 14:1 (1973), 102–122; Theoret. and Math. Phys., 14:1 (1973), 75–89
This publication is cited in the following 22 articles:
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Quinn E., “On Non-Canonical Degrees of Freedom”, SciPost Phys., 10:3 (2021), 075
A. V. Mokshin, “Self-consistent approach to the description of relaxation processes in classical multiparticle systems”, Theoret. and Math. Phys., 183:1 (2015), 449–477
O.A. Kotelnikova, V.N. Prudnikov, Yu.G. Rudoy, “Magnetocaloric effect (MCE): Microscopic approach within Tyablikov approximation for anisotropic ferromagnets”, Journal of Magnetism and Magnetic Materials, 383 (2015), 203
N. M. Plakida, “The two-time Green's function and the diagram technique”, Theoret. and Math. Phys., 168:3 (2011), 1303–1317
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
Daisuke Yamamoto, Synge Todo, Susumu Kurihara, “Green's function theory for spin-12ferromagnets with an easy-plane exchange anisotropy”, Phys. Rev. B, 78:2 (2008)
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
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
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
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
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
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
Yu. G. Rudoi, “Quasicollective spin waves in the paramagnetic region of an anisotropic Heisenberg ferromagnet”, Theoret. and Math. Phys., 26:3 (1976), 263–269
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
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
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
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
H. Englisch, A. Kühnel, G. Miethe, “Exact Solution of Dembinski's Decoupling Scheme for the Heisenberg Ferromagnet”, Physica Status Solidi (b), 67:1 (1975)
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
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