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Recently, we have numerically evaluated the current-current correlationfunction for the ground states of three-band models for the CuO planes ofhigh-Tc superconductors at hole doping x=1/8 using systems with 24 sites andperiodic boundary conditions. In this article, the numerical analysis isexplicated in detail and extended to a wider range of parameters. Our resultsshow no evidence for the time-reversal symmetry violating current patternsrecently proposed by Varma. If such current patterns exist, our resultsindicate that the energy associated with the loop currents must be smaller than5 meV per link even if the on-site chemical potential on the oxygen sites,which is generally assumed to be of the order of 3.6 eV, is taken to zero, asadvocated by Varma. We also vary the inter-atomic Coulomb repulsion scale andfind only a weak dependence on this parameter. So while our studies do not ruleout the existence of such current patterns, they do rule out that quantumcritical fluctuations of these patterns are responsible for phenomena occurringat significantly higher energies such as the superconductivity or the anomalousproperties observed in the strange metal phase provided the CuO superconductorsare adequately described by any of the three-band models discussed.

Numerical analysis of three-band models for CuO planes as candidates for a spontaneous T violating orbital current phase