No evidence for spontaneous orbital currents in finite size studies of three-band models for CuO planes

We have numerically evaluated the current-current correlations for three-band models of the CuO planes in high-T_c superconductors at hole doping x=1/8. The results show no evidence for the orbital current patterns proposed by Varma. If such patterns exist, the associated energy is estimated to be smaller than 5 meV per link even if epsilon_p-epsilon_d=0. Assuming that the three-band models are adequate, quantum critical fluctuations of such patterns hence cannot be responsible for phenomena occurring at significantly higher energies, such as superconductivity or the anomalous properties of the pseudogap phase.