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

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application II: Hubbard model (N c = 1)<br />

Hubbard model: H = −t ∑ 〈i,j〉,σ (c† i,σ c j,σ + h.c.) + U ∑ i n i,↑n i,↓<br />

-0.46<br />

-0.47<br />

Exact<br />

SC 2nd-order<br />

FLEX<br />

PA<br />

G(τ)<br />

-0.48<br />

-0.49<br />

U/T=1.5, Nc=1, Nl=64<br />

-0.5<br />

0 0.2 0.4 0.6 0.8 1<br />

τ/β<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 37

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