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Volumn 86, Issue 12, 2012, Pages

Local electronic correlation at the two-particle level

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EID: 84866434914     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.86.125114     Document Type: Article
Times cited : (261)

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    • This can be easily seen by the following argument: Consider a diagram that is reducible in one of the two particle-hole channels as that shown in Fig. It is evident that the subdiagram A can be separated from B by cutting the Green's function lines a and b. Let us assume that the diagram is reducible in the (1 4)-(2 3) channel as well, i.e., it can be split into two parts, one containing the outer legs 1 and 4 the other one containing 2 and 3 by cutting two internal lines. This would be only possible if the subdiagrams A and B could be split into two parts by cutting only one internal line. But, this is impossible since it would lead to subdiagrams with three outer legs, which violates particle conservation. Therefore, it is proven that each diagram is either fully irreducible or reducible in exactly one channel.
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