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I'm interested in the possible limitations of the Random Phase Approximation (RPA). When is it expected to fail? As I understand it, RPA can be derived from the GW approximation, as can be seen here, and its physical meaning is that we treat the response of the total field to a perturbation as if the system was not interacting (this is a great explanation of that point of view, the functional derivative technique and the closely related Hedin equations).

So, my question is, in what sort of systems or under which conditions can this approximation be expected to be bad or very bad? The only similar question I've found on the site is this, but I don't feel it answers the question.

I'm more confused when I look at this from the point of view of diagrams: If I forget about what I wrote above, what is the justification for ignoring the no-ring driagrams? Considering just second order, for instance, I know for sure some particular cases where there are no-ring diagrams which add important contributions, so this confuses me.

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  • $\begingroup$ Have you seens Chapter. 5 of Altland and Simons, they give some justification to RPA. $\endgroup$
    – Sunyam
    Oct 5, 2018 at 9:58
  • $\begingroup$ No, I haven't. Thanks for the tip, I'll check it out. $\endgroup$
    – Qwertuy
    Oct 6, 2018 at 14:28

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