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Update theory
authored
Jan 30, 2025
by
Johannes Wasmer
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@@ -45,6 +45,7 @@ R_{i\ell}\^\sigma(r;E_\text{F})$.
### Kohn-Sham susceptibility
The transverse magnetic Kohn-Sham susceptibility is given by
```
math
\chi^{\sigma\bar{\sigma}}_{0,ij}(\vec{r}\,,\vec{r}\,';\omega)
&=& -\frac{1}{\pi}\!\int^{E_\text{F}}\!\!\!\!\text{d}E \nonumber \\
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@@ -63,6 +64,7 @@ $\chi\^{-+}$, respectively.
Let us turn our attention to the Dyson equation for the GF, including
the self-energy describing the coupling to the magnetic excitations:
```
math
G_{ij}^\sigma(\vec{r}\,,\vec{r}\,';E)
&=& G_{0,ij}^\sigma(\vec{r}\,,\vec{r}\,';E) + \sum_{pq}\!\int\!\!\text{d}\vec{r}_1\!\int\!\!\text{d}\vec{r}_2\; \times \nonumber\
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