Charge Gap in the One-Dimensional Extended Hubbard Model at Quarter Filling

TL;DR

This paper introduces a combined computational approach to accurately estimate the charge gap in a one-dimensional extended Hubbard model at quarter filling, especially near the metal-insulator transition where the gap is exponentially small.

Contribution

The paper presents a novel combined method integrating exact diagonalization, renormalization group, and Bethe ansatz to precisely determine the charge gap including its prefactor.

Findings

Accurate charge gap estimates down to 10^{-10} near the MIT.

Contour maps of the charge gap on the U-V parameter plane.

Method surpasses traditional RG and finite size scaling in critical regimes.

Abstract

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