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Hierarchy of Self-Consistent Approximate Methods and the Parquet ...

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summary <strong>of</strong> <strong>the</strong> different approximate methods<br />

G<br />

Σ<br />

⇐ F = 0<br />

HF<br />

G<br />

Σ<br />

⇐ F ≈ v<br />

SOP T<br />

G<br />

⇐ Γ ≈ v<br />

RP A, T MA, F LEX<br />

Σ<br />

F<br />

G<br />

Γ<br />

P A<br />

⇐ Λ ≈ v<br />

MSMB<br />

Λ II ≈ Λ I,DCA/QMC<br />

Σ<br />

F<br />

• iterate until self-consistency is satisfied<br />

• It is also a hierarchy <strong>of</strong> methods with different computational costs<br />

• <strong>the</strong>re are two levels <strong>of</strong> self-consistency for <strong>the</strong> parquet calculation<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 34

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