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