Phase diagram of the one-dimensional extended Hubbard model at quarter filling

TL;DR

This paper maps the phase diagram of the 1D extended Hubbard model at quarter filling, revealing transitions between metallic, charge-density wave, and insulating phases, with detailed critical exponents and fluctuation behaviors.

Contribution

It provides the first comprehensive phase diagram and critical exponent analysis of the 1D $U-V$ model at quarter filling using exact diagonalization and limit results.

Findings

Instability of Luttinger liquid to CDW insulator across a specific boundary.

Superconducting fluctuations dominate in the metallic phase for large V.

Critical exponent $oldsymbol{ extalpha}$ does not exceed 9/16 in SDW phase.

Abstract

We used exact diagonalization of small clusters and exact results in various limits to determine the phase diagram and the critical exponents of the one dimensional (1D) $U-V$ model at quarter-filling. We found an instability of the Luttinger liquid to a charge-density wave (CDW) insulator across a boundary going from ($U$,$V$) =($+\infty$,$2t$) to ($4t$,$+\infty$). In the metallic phase, the dominant fluctuations are superconducting if $V$ is large enough and spin-density wave (SDW) otherwise. In the latter case, the critical exponent $\alpha$ of the momentum distribution does not exceed 9/16. The relevance of these results to 1D organic conductors is discussed.