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

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Hartree-Fock approximation: F = 0<br />

• No vertex correction to <strong>the</strong> self-energy<br />

• 〈n i↑ n i↓ 〉 = 〈n i↑ 〉〈n i↓ 〉 (χ = G ∗ G)<br />

• Lowest-order correction: O(U 2 )<br />

Σ<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 24

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