Correlation function for the one-dimensional extended Hubbard model at quarter filling

TL;DR

This paper derives an analytical form of the density-density correlation function in a one-dimensional extended Hubbard model at quarter filling, revealing a crossover between different power-law behaviors influenced by charge ordering.

Contribution

It introduces a generalized analytical expression for the correlation function considering marginally irrelevant operators using bosonization and RG techniques, validated by DMRG simulations.

Findings

Crossover between power-law and logarithmic-corrected power-law behavior.

Analytical form matches numerical DMRG results.

Proximity to charge-ordered phase influences correlation decay.

Abstract

We examine the density-density correlation function in the Tomonaga-Luttinger liquid state for the one-dimensional extended Hubbard model with the on-site Coulomb repulsion $U$ and the intersite repulsion $V$ at quarter filling. By taking into account the effect of the marginally irrelevant umklapp scattering operator by utilizing the renormalization-group technique based on the bosonization method, we obtain the generalized analytical form of the correlation function. We show that, in the proximity to the gapped charge-ordered phase, the correlation function exhibits anomalous crossover between the pure power-law behavior and the power-law behavior with logarithmic corrections, depending on the length scale. Such a crossover is also confirmed by the highly-accurate numerical density-matrix renormalization group method.