pdf, 9 MiB - Infoscience - EPFL
pdf, 9 MiB - Infoscience - EPFL
pdf, 9 MiB - Infoscience - EPFL
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6.10. VMC ON LARGE LATTICES 163<br />
M=()0.5<br />
0.2<br />
108<br />
192<br />
300<br />
sites<br />
sites<br />
sites<br />
0.0<br />
-0.2<br />
0.0<br />
hole doping n<br />
h<br />
0.2<br />
0.4<br />
√<br />
Figure 6.18: Magnetic order parameter M = lim r→∞ 〈S<br />
z<br />
i Si+ z 〉) versus the hole<br />
doping. The saturated value for the magnetic order parameter is M =0.5.<br />
pure local gutzwiller projection, which kills very strongly the kinetic energy. Another<br />
way to reduce the double occupancy is done by the resonating valence bond<br />
instability, which optimizes both the double occupancy and the kinetic energy.<br />
We show in Fig. 6.14 the energy gains of the SDW and RVB instabilities when<br />
no projection are present. The two instabilities cross at around x ≈ 20% doping.<br />
However, the correlated part of the wavefunction plays a drastic role and clearly<br />
needs to be considered. Very interestingly, we find that the symmetry of the<br />
pairing ∆ ij is, in the real space representation of the three-band Hubbard model,<br />
not restricted to nearest neighbor copper and oxygen sites. Indeed, no energy<br />
optimization can be obtained when the pairing is restricted to oxygen-oxygen<br />
and copper-oxygen bonds. This can be understood in terms of the Zhang-Rice<br />
mapping of the three-band Hubbard model to the one band t−J model. In the<br />
frame of this theory, the particles of the t−J model are equivalent to a local<br />
copper-oxygen d ↑ (p x↓ − p −x↓ + p y↓ − p −y↓ ) singlet in the three-band language. It<br />
was very strongly established that a d-wave RVB instability is present in the t−J<br />
model [19, 144, 24, 129], but it is not intuitive to get a picture of this supercon-