Abstract
The random-phase approximation (RPA) has been widely used for studying linear responses to external perturbations and describing elementary excitations.
The next approximation... goes under a wide variety of names (random phase approximation, independent-pair approximation, self-consistent field approximation, time-dependent Hartree–Fock approximation, etc.); in fact, there are almost as many names as there are ways of deriving the answer. We shall arbitrarily refer to it as the random phase approximation, or RPA. (D. Pines, Elementary Excitations in Solids, Benjamin, New York, 1964)
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Notes
- 1.
Use of the complex field rather than real one \(\mathbf{H}(\mathbf{r},t) =\hat{ \mathbf{z}}H_{z}(\mathbf{q})\,\cos (\mathbf{qr})\cos \omega t\) (see, e.g. [5]) largely simplifies the derivation.
- 2.
Poles of χ −+(q, ω) give an equation that corresponds to the spin waves precessing in the opposite direction.
- 3.
This simple form of the spin-wave spectrum is in good agreement with neutron scattering experiments (see, e.g. [18]).
- 4.
These singularities are called the branch cuts (for details, see Appendix A.2.4).
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Melnikov, N.B., Reser, B.I. (2018). Random-Phase Approximation. In: Dynamic Spin-Fluctuation Theory of Metallic Magnetism. Springer, Cham. https://doi.org/10.1007/978-3-319-92974-3_5
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