Phase diagram of the one-dimensional extended Hubbard model with attractive and/or repulsive interactions at quarter filling

TL;DR

This paper maps the complex phase diagram of the 1D extended Hubbard model at quarter filling, revealing eight phases including insulating, phase-separated, and superconducting states, using numerical and analytical techniques.

Contribution

It provides the first comprehensive phase diagram for the 1D U-V model at quarter filling, identifying four novel phases not seen in weak coupling.

Findings

Eight distinct phases identified in the phase diagram.

Discovery of a phase with dominant superconducting fluctuations without a spin gap.

Identification of insulating and phase-separated regions depending on U and V.

Abstract

We study the phase diagram of the one dimensional (1D) $U-V$ model at quarter filling in the most general case where the on-site and first-neighbour interactions $U$ and $V$ can be both attractive and repulsive. The results have been obtained using exact diagonalization of small clusters and variational techniques, as well as exact results in various limits. We have analyzed four properties of the groundstate: i)~whether it is insulating or metallic; \hbox{ii)~whether} it is homogenous or phase separated; iii)~whether it has a spin gap; iv)~whether it has dominant superconducting fluctuations. With eight phases, the resulting phase diagram is unexpectedly rich. The four phases not found in the weak coupling limit are: i) an insulating phase when $U$ and $V$ are large enough; ii) a region of phase separation when $V$ is attractive; iii) another region of phase separation when $V$ is large enough and $U$ small; iv) a region with dominant superconducting fluctuations when $V$ is intermediate and $U$ small. The actual nature of this last phase, which has pairs but no spin gap, is not fully clear yet.