Hierarchy of Self-Consistent Approximate Methods and the Parquet ...
Hierarchy of Self-Consistent Approximate Methods and the Parquet ...
Hierarchy of Self-Consistent Approximate Methods and the Parquet ...
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<strong>Self</strong>-<strong>Consistent</strong> Diagrammatic Calculation<br />
• Conventional perturbation calculation (Green function G based)<br />
⊲ G = G[G 0 , U], e.g., 1st-order (Hartree)<br />
• Conventional perturbation calculation (self-energy Σ based)<br />
⊲ Σ = Σ[G 0 , U]<br />
⊲ G = G 0<br />
1−ΣG 0<br />
• <strong>Self</strong>-<strong>Consistent</strong> Diagrammatic Calculation<br />
⊲ Σ = Σ[G, U, F ]<br />
⊲ G = G 0<br />
+ + +<br />
G<br />
Σ =<br />
1−ΣG 0<br />
Σ<br />
1st iter<br />
+ +<br />
+<br />
2nd iter<br />
+ + +<br />
<strong>Hierarchy</strong> <strong>of</strong> <strong>Self</strong>-<strong>Consistent</strong> <strong>Approximate</strong> <strong>Methods</strong> <strong>and</strong> <strong>the</strong> <strong>Parquet</strong> Formalism 6
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