Impurity in a Luttinger liquid away from half-filling: a numerical study

TL;DR

This paper numerically investigates impurity effects in a quarter-filled Luttinger liquid, confirming conformal field theory predictions and extending their validity beyond half-filling.

Contribution

It provides the first numerical verification of conformal field theory predictions for impurity effects away from half-filling in Luttinger liquids.

Findings

Numerical results agree with conformal field theory predictions

Validates theoretical models for arbitrary fillings

Extends understanding of impurity effects in Luttinger liquids

Abstract

Conformal field theory gives quite detailed predictions for the low energy spectrum and scaling exponents of a massless Luttinger liquid at generic filling in the presence of an impurity. While these predictions were verified for half-filled systems, there was till now no analysis away from this particular filling. Here, we fill in this gap by numerically investigating a quarter-filled system using the density matrix renormalization group technique. Our results confirm conformal field theory predictions, and suggest that they are indeed valid for arbitrary fillings.