Time-reversal symmetry breaking phase in the Hubbard model: A variational cluster approach study

We study the stability of the time-reversal symmetry breaking staggered-flux phase of a single band Hubbard model, within the variational cluster approach. 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 approximate to 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-neighbor interaction is also considered. Our results show that a negative nearest-neighbor 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.