Renormalization-group analysis of the one-dimensional extended Hubbard model with a single impurity

TL;DR

This paper uses a functional renormalization group approach to analyze how a single impurity affects the electronic properties of the one-dimensional extended Hubbard model with spin-1/2 fermions, revealing complex impurity-induced effects.

Contribution

It extends previous spinless fermion studies to include spin-1/2 fermions and examines impurity effects using a novel computational technique validated against DMRG data.

Findings

Two-particle backscattering causes notable effects not seen in the low-energy fixed point.

Spectral weight near the impurity can initially increase before decreasing at low energies.

Logarithmic corrections modify the expected power-law behavior of conductance.

Abstract

We analyze the one-dimensional extended Hubbard model with a single static impurity by using a computational technique based on the functional renormalization group. This extends previous work for spinless fermions to spin-1/2 fermions. The underlying approximations are devised for weak interactions and arbitrary impurity strengths, and have been checked by comparing with density-matrix renormalization-group data. We present results for the density of states, the density profile and the linear conductance. Two-particle backscattering leads to striking effects, which are not captured if the bulk system is approximated by its low-energy fixed point, the Luttinger model. In particular, the expected decrease of spectral weight near the impurity and of the conductance at low energy scales is often preceded by a pronounced increase, and the asymptotic power laws are modified by logarithmic corrections.