Orthogonality catastrophe in a one-dimensional system of correlated electrons

TL;DR

This paper numerically investigates the orthogonality catastrophe in a one-dimensional system of correlated spinless fermions, analyzing impurity effects and confirming theoretical scaling behaviors with high accuracy.

Contribution

It provides a detailed numerical analysis of the orthogonality catastrophe exponent in a 1D correlated electron system, clarifying finite size effects and impurity influences.

Findings

Weak impurity limit matches perturbation theory predictions.

Backward scattering exponent scales to zero for attractive interactions.

Finite size effects hinder exponent extraction in strong impurity and repulsive cases.

Abstract

We present a detailed numerical study of the orthogonality catastrophe exponent for a one-dimensional lattice model of spinless fermions with nearest neighbor interaction using the density matrix remormalization group algorithm. Keeping up to 1200 states per block we achieve a very great accuracy for the overlap which is needed to extract the orthogonality exponent reliably. We discuss the behavior of the exponent for three different kinds of a localized impurity. For comparison we also discuss the non-interacting case. In the weak impurity limit our results for the overlap confirm scaling behavior expected from perturbation theory and renormalization group calculations. In particular we find that a weak backward scattering component of the orthogonality exponent scales to zero for attractive interaction. In the strong impurity limit and for repulsive interaction we demonstrate that the orthogonality exponent cannot be extracted from the overlap for systems with up to 100 sites, due to finite size effects. This is in contradiction to an earlier interpretation given by Qin et al. based on numerical data for much smaller system sizes. Neverthless we find indirect evidence that the backward scattering contribution to the exponent scales to 1/16 based on predictions of boundary conformal field theory.