pdf, 9 MiB - Infoscience - EPFL
pdf, 9 MiB - Infoscience - EPFL
pdf, 9 MiB - Infoscience - EPFL
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160 CHAPTER 6. ORBITAL CURRENTS IN THE CUPRATES<br />
0.0<br />
(E-E Gutzwiller<br />
)/N Copper<br />
-0.1<br />
-0.2<br />
-0.3<br />
-0.4<br />
JA/FLUX, 192 sites<br />
JA, 192 sites<br />
FLUX, 192 sites<br />
SDW, 192 sites<br />
FLUX, 108 sites<br />
0.00<br />
0.05<br />
0.10<br />
0.15<br />
0.20<br />
0.25<br />
hole doping n<br />
h<br />
0.30<br />
0.35<br />
0.40<br />
Figure 6.16: Energy difference between the different variational Ansatz and the<br />
Gutzwiller wavefunction. Open boundary conditions are assumed in these calculations.<br />
a ring coupled to an external flux [143] is minimized in finite-size rings at integer<br />
values of the flux quanta. The ring can be seen as a one dimensional chain with<br />
periodic boundary conditions and therefore it has also in this case a net current<br />
running through the boundary conditions. In conclusion, models with artificial<br />
flux through the boundary conditions are known to introduce corrections to the<br />
energy for finite-size clusters. Therefore, the small energy optimization of the<br />
JA/FLUX wavefunction could well be due to a finite-size effect. However, there<br />
is a subtle but crucial difference between comparing the energy of the groundstates<br />
of Hamiltonians with different periodic/anti-periodic conditions, or having<br />
different flux imposed, and comparing for a given model the energy of different<br />
variational wavefunction. In the former case, the parameters of the model are<br />
changed, and a finite flux through the boundary conditions is stabilized in the<br />
ground state. But this flux is already introduced in the original Hamiltonian, and<br />
it is natural to observe it in the ground state. In the latter case, the Hubbard<br />
Hamiltonian does not contain any flux originally, but the variational Ansatz opti-