Tricritical Behavior in the Extended Hubbard Chains

TL;DR

This paper investigates the phase transitions and tricritical behavior in the one-dimensional extended Hubbard model at different fillings, revealing complex phase diagrams with BKT, Gaussian, and spin-gap transitions, and the emergence of a BCDW phase.

Contribution

The study provides high-accuracy phase boundary determination using level crossings and explores the effects of correlated hopping on phase stability and transitions.

Findings

Identification of two BKT and one Gaussian transition line at half-filling.

Discovery of a tricritical point where charge and spin transitions couple.

Observation of a crossover involving spin-gap and metal-insulator transitions at quarter-filling.

Abstract

Phase diagrams of the one-dimensional extended Hubbard model (including nearest-neighbor interaction $V$) at half- and quarter-filling are studied by observing level crossings of excitation spectra using the exact diagonalization. This method is based on the Tomonaga-Luttinger liquid theory including logarithmic corrections which stem from 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 region. This result demonstrates existence of a tricritical point and a bond-charge-density-wave (BCDW) phase between charge- and spin-density-wave (CDW, SDW) phases. To clarify this mechanism of the transition, we also investigate effect of a correlated hopping term which plays a role to enlarge BCDW and bond-spin-density-wave (BSDW) phases. At quarter-filling, a similar crossover phenomenon also takes place in the large-$V$ region involving spin-gap and BKT-type metal-insulator transitions.