Finite-size scaling of correlation functions in one-dimensional Anderson-Hubbard model

TL;DR

This paper investigates how disorder affects correlation functions in the one-dimensional Anderson-Hubbard model, revealing how disorder and interactions influence localization and charge behavior.

Contribution

It provides a finite-size scaling analysis of correlation functions, showing disorder reduces charge exponents and that localization length scales as the inverse square of disorder strength.

Findings

Charge exponent decreases with disorder at low and half filling.

Localization length scales as Δ^{-2} regardless of interactions.

Coulomb interaction suppresses localization near half filling.

Abstract

We study the one-dimensional Anderson-Hubbard model using the density-matrix renormalization group method. The influence of disorder on the Tomonaga-Luttinger liquid behavior is quantitatively discussed. Based on the finite-size scaling analysis of density-density correlation functions, we find the following results: i) the charge exponent is significantly reduced by disorder at low filling and near half filling, ii) the localization length decays as $\xi \sim \Delta^{-2}$, where $\Delta$ is the disorder strength, independently of the on-site Coulomb interaction as well as band filling, and iii) the localization length is strongly suppressed by the on-site Coulomb interaction near half filling in association with the formation of the Mott plateaus.