Abstract
Solid systems present fascinating and intriguing phenomena whose physical origin is underlined by the complicated motions and interactions among the collections of electrons and nuclei
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- 1.
We remind the reader that \(\hat{\mathcal {H}}\), \(\nu \), and \(\hat{N}\) are the many-body Hamiltonian, the chemical potential, and the particle number operator of the entire solid problem, respectively.
- 2.
Note that \(\underline{R}=\underline{I}_2\cos (\theta _{\hat{e}_n}/2)-i\sigma _j\sin (\theta _{\hat{e}_n}/2)\), where \(\theta _{\hat{e}_n}\) is the angle between \(\hat{e}_n\) and the \(\hat{z}\)-axis, in the frame of reference of \(\underline{t}_n^\text {ref}\), and \(\sigma _j\) indicates the direction of rotation.
- 3.
In this step we have used the equality \(\det (A+B)=\det A+\det B+\det B\text {Tr}(AB^{-1})\) and neglected a term that does not contribute to \(S^{(2)}_{ij}\).
- 4.
Here we have considered the inverse matrix property \(\frac{\partial A^{-1}}{\partial \alpha }=-A^{-1}\frac{\partial A}{\partial \alpha }A^{-1}\) too.
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Mendive Tapia, E. (2020). Disordered Local Moment Theory and Fast Electronic Responses. In: Ab initio Theory of Magnetic Ordering. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-37238-5_3
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DOI: https://doi.org/10.1007/978-3-030-37238-5_3
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