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194 APPENDIX B. A PAIR OF PARTICLES IN A CUO 4 CLUSTER
Nevertheless, we found in the three-band Hubbard model that the wavefunction
with (α 1 ,α 2 ) lying in the long-dashed rectangular box of Fig.B.2 was optimal.
This later wavefunction has a current pattern which is similar to the θ 2
phase of C.Varma, but has reversed current lines on the oxygen-oxygen bonds,
and the amplitude of these lines is small. On the other hand, we measured the
corresponding mean-field operator that are defined by :
ĵ MF
kl
= ∑ σ
it kl e iθ kl
c † iσ c jσ + c.c.
(B.11)
ˆK MF
kl
= ∑ σ
t kl e iθ kl
c † iσ c jσ + c.c.
(B.12)
We show in Fig.B.3 the range of parameters (α 1 ,α 2 ) that are stabilized in variational
Monte-Carlo calculations (short-dashed rectangular box). For the corresponding
range of parameters the mean-field current operator is identical to
the θ 2 phase of C. Varma, with strong currents on the oxygen-oxygen bonds. In
conclusion, the variational calculations stabilize a wavefunction that has a flux
through the periodic boundaries and a weak current on the oxygen-oxygen links
when the physical current observable ĵ is considered, but the same wavefunction
would have a true current circulation inside the triangle plaquettes when the
mean-field current operator j MF is measured in this same wavefunction.