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

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 until 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.