Understanding correlations and localization in the Hubbard model ...
Understanding correlations and localization in the Hubbard model ...
Understanding correlations and localization in the Hubbard model ...
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GA applied to BWF: <strong>in</strong>teraction<br />
Rewrite hopp<strong>in</strong>g <strong>in</strong> k space<br />
(<br />
∑<br />
n i↑ n i↓ = 1 ∑<br />
ñ k↑ ñ k<br />
L<br />
′ ↓ − ∑<br />
k,k ′<br />
i<br />
kk ′ q≠0<br />
˜c † k↑˜c† k ′ ↓˜c k+q↑˜c k ′ −q↓<br />
)<br />
.<br />
〈<br />
〉<br />
˜c † k↑˜c† k ↓˜c k+q↑˜c ′ k ′ −q↓<br />
=<br />
B<br />
∑ ′′<br />
Γ P GA−B[Γ]{e −α(ǫ k Γ<br />
+ǫ k ′ −ǫ Γ kΓ +q Γ<br />
−ǫ k ′ Γ −q ) Γ }<br />
∑<br />
Γ P ,<br />
GA−B[Γ]<br />
<strong>Underst<strong>and</strong><strong>in</strong>g</strong> <strong>correlations</strong> <strong>and</strong> <strong>localization</strong> <strong>in</strong> <strong>the</strong> <strong>Hubbard</strong> <strong>model</strong> from variational calculations – p. 22