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

Abstract

We propose a different combined approach, which consists of the exact diagonalization, renormalization group, and Bethe ansatz methods, for precise estimates of the charge gap $\ensuremath{\Delta}$ in the one-dimensional extended Hubbard model, with on-site and nearest-neighbor interactions $U$ and $V$ at quarter filling. This approach enables us to obtain the absolute value of $\ensuremath{\Delta}$, including the prefactor, without ambiguity even in the critical regime of the metal-insulator transition (MIT) where $\ensuremath{\Delta}$ is exponentially small, beyond usual renormalization group methods and/or finite-size scaling approaches. The detailed results of $\ensuremath{\Delta}$, down to the order of ${10}^{\ensuremath{-}10}$ near the MIT, are shown as contour lines on the $U\text{\ensuremath{-}}V$ plane.