Tricritical Behaviors in the Extended Hubbard Chains

The phase diagrams of the one-dimensional extended Hubbard model at half- and quarter-filling are studied by observing the level crossing of the excitation spectra using the exact diagonalization. This method is based on the Tomonaga-Luttinger liquid theory including the logarithmic corrections which stems form the renormalization of the Umklapp and the backward scattering effects. Using this approach, the phase boundaries are determined with high accuracy, and then the structure of the phase diagram is clarified. At half-filling, the phase diagram consists of two Berezinskii-Kosterlitz-Thouless (BKT) transition lines and one Gaussian transition line in the charge sector, and one spin-gap transition line. This structure reflects the U(1) $\otimes$ SU(2) symmetry of the electron system. Near the $U=2V$ line, the Gaussian and the spin-gap transitions take place independently from the weak- to the intermediate-coupling region, but these two transition lines are coupled in the strong-coupling regime. This result demonstrates the existence of a tricritical point and a bond-order-wave (BOW) phase between the charge- and spin-density-wave (CDW, SDW) phases. To clarify this mechanism of the transition, we also investigate the effect of the correlated hopping term which plays a role to enlarge the BOW phase. At quarter-filling, a similar crossover phenomenon also takes place in the large-$V$ region involving the spin-gap and the BKT-type metal-insulator transitions.