Combined Analysis of Numerical Diagonalization and Renormalization Group methods for the One-Dimensional $U$-$V$ Model at Quarter filling

TL;DR

This paper combines numerical diagonalization and renormalization group methods to analyze the one-dimensional extended Hubbard model at quarter filling, accurately predicting properties like the Luttinger-liquid parameter and charge gap.

Contribution

It introduces a novel finite size scaling approach that integrates diagonalization with RG to study the U-V model at quarter filling, especially near phase transitions.

Findings

Accurately computes the Luttinger-liquid parameter $K_\rho$ for infinite systems.

Predicts the charge gap near the metal-insulator transition.

Results agree well with known exact solutions for $U=\infty$.

Abstract

The one-dimensional extended Hubbard model with both the on-site $U$ and the nearest neighbor $V$ interactions at quarter filling is studied by using a novel finite size scaling. We diagonalize finite size systems numerically and calculate the Luttinger-liquid parameter $K_{\rho}$ which is substituted into the renormalization group equation as an initial condition. It leads $K_\rho$ in the infinite size system and the result agrees very well with the available exact result with $U=\infty$. This approach also yields the charge gap in the insulating state near the metal-insulator transition where the characteristic energy becomes exponentially small and the usual finite size scaling is not applicable.