Pseudogap phase: Exchange energy driven versus kinetic energy driven

In this paper, we comparatively study two mean-field theories of pseudogap phase based on the t-J model. We find that while the pseudogap phase is superexchange-energy-driven in the slave-boson resonating-valence-bond (RVB) state, it is kinetic-energy-driven in the bosonic RVB state. The sharp contrast in the mechanisms of the pseudogap phases can be attributed to the fact that the antiferromagnetic (AF) correlations behave quite differently in two mean-field states, which in turn distinctly influence the kinetic energy of charge carriers. We elaborate this based on some detailed studies of the superexchange energy, kinetic-energy, uniform spin susceptibility, equal-time spin correlations, dynamic spin susceptibility, as well as the optical conductivity. The results provide a consistent picture and understanding on two physically opposite origins of pseudogap phase. We argue that both kinetic and superexchange energies of the t-J model may be. read off from the optical data, based on an optical sum rule for the Hubbard model. In comparison with experimental measurements, we are led to conclude that the pseudogap phase described in the bosonic RVB state as kinetic-energy-driven is consistent with the experiment.