pdf, 9 MiB - Infoscience - EPFL
pdf, 9 MiB - Infoscience - EPFL
pdf, 9 MiB - Infoscience - EPFL
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
6.3. THREE-BAND HUBBARD MODEL 137<br />
Figure 6.3: The gauge choice in the Lanczos calculations. the d x2−y2 and p σ<br />
orbitals are shown. The phases due to the hybridization in this gauge are S dp =<br />
−1 for the copper-oxygen links, and S pp = −1 for the oxygen-oxygen links. In<br />
this gauge choice, the signs of the transfer integrals do not anymore break the 90 ◦<br />
rotational symmetry. This latter symmetry is used in the Lanczos calculations<br />
as an additional quantum number, that allows to diagonalize the Hamiltonian<br />
matrix in smaller blocks of the Hilbert space.<br />
t dp +<br />
- +<br />
p y<br />
- -<br />
+<br />
-<br />
+<br />
t pp<br />
d x 2 -y 2<br />
p x<br />
Figure 6.4: A single CuO 2 layer, the copper are indicated as large sphere, and<br />
the oxygens as small one. The system has one hole per copper site at half-filling.<br />
Both the transfer integral t dp between the d x 2 −y 2 and the p x,y orbitals and the<br />
transfer integral t pp between the p x and the p y orbitals are considered. In hole<br />
notations the bonding orbitals enter the Hamiltonian with a positive transfer<br />
integral sign, and the anti-bonding orbitals with a negative sign. The signs of<br />
the t pp and t dp transfer integrals are shown.