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Extending the random phase approximation with renormalized ...

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Spin<br />

There is not a unique way to generalize to spin-polarized systems<br />

For a spinpaired system it is straightforward to show that<br />

=[ ALDA<br />

f Hx<br />

f Hxc = 1<br />

4 ∑σ σ ' f σ σ '<br />

Hxc<br />

The ALDA Hartree-exchange kernel is<br />

V +2f ALDA<br />

x [2n↑ ] V<br />

V V +2f x<br />

ALDA [2n↓]]<br />

It is clear that we cannot simply introduce cutoff on <strong>the</strong> diagonal

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