Charge gap in the one--dimensional dimerized Hubbard model at quarter-filling

TL;DR

This paper provides a comprehensive analytical and numerical estimate of the charge gap in the one-dimensional dimerized Hubbard model at quarter-filling, relevant for understanding electronic properties of certain organic salts.

Contribution

It introduces a unified estimate of the charge gap valid across all interaction and dimerization strengths, combining analytical limits and numerical exact diagonalization results.

Findings

Charge gap estimate applicable for any repulsion and dimerization parameters.

Analytical results derived in weak, strong, and large dimerization limits.

Numerical validation using exact diagonalization of small clusters.

Abstract

We propose a quantitative estimate of the charge gap that opens in the one-dimensional dimerized Hubbard model at quarter-filling due to dimerization, which makes the system effectively half--filled, and to repulsion, which induces umklapp scattering processes. Our estimate is expected to be valid for any value of the repulsion and of the parameter describing the dimerization. It is based on analytical results obtained in various limits (weak coupling, strong coupling, large dimerization) and on numerical results obtained by exact diagonalization of small clusters. We consider two models of dimerization: alternating hopping integrals and alternating on--site energies. The former should be appropriate for the Bechgaard salts, the latter for compounds where the stacks are made of alternating $TMTSF$ and $TMTTF$ molecules. % $(TMTSF)_2 X$ and $(TMTTF)_2 X$ ($X$ denotes $ClO_4$, $PF_6$, $Br$...).