Variational tests of current order parameters in the Hubbard model

Variational tests are performed for current order parameters as probable sources of the pseudogap normal state of cuprates. The calculations are carried out based on the states with correlations of the valence bond type whose formation can induce in principle both the superconducting order of the d symmetry and current phases. It is shown for the t-t′-U Hubbard models with a large value of U(～8t) and the Hubbard splitting of the conduction band that (1) phases of alternating charge and longitudinal spin currents cannot be realized and (2) transverse spin currents are not compatible with the superconducting order and they could exist against the normal-state background only within a very narrow doping region near the optimal one. This region does not correspond to the region of existence of a pseudogap in cuprates, which refutes the above-mentioned hypothesis of the pseudogap origin. The requirements to the parameters of models for which the consideration of correlations of the valence bond type yields a reasonable phase curve. The existence of current phases in the t-t′-U-V Hubbard models with a strong interaction (V>0.25t) of particles in neighboring sites is predicted when the d-superconductivity is completely suppressed.