  We study the stability of the time-reversal symmetry breaking staggered flux
phase of a single band Hubbard model, within the Variational Cluster Approach
(VCA). For intermediate and small values of the interaction $U$, we find
metastable solutions for the staggered flux phase, with a maximum current per
bond at $U\approx 3.2$. However, allowing for antiferromagnetic and
superconducting long-range order it turns out that in the region at and close
to half filling the antiferromagnetic phase is the most favorable
energetically. The effect of nearest-neighbour interaction is also considered.
Our results show that a negative nearest-neighbour interaction and finite
doping favors the stability of the staggered-flux phase. We also present
preliminary results for the three-band Hubbard model obtained with a restricted
set of variational parameters. For this case, no spontaneous time-reversal
symmetry breaking phase is found in our calculations.
