Threshold singularities in the correlators of the one-dimensional models

TL;DR

This paper analyzes threshold singularities in one-dimensional models using non-linear Luttinger liquid form factors, explaining why simplified impurity models yield correct results and deriving k-dependent prefactors at small momentum.

Contribution

It introduces a method to calculate threshold singularities in 1D models using universal form factors within the non-linear Luttinger liquid framework, clarifying the validity of simplified impurity pictures.

Findings

Derived the k-dependent prefactors of singularities at small k

Explained the correctness of simplified impurity models in Luttinger liquids

Calculated threshold singularities using universal form factors

Abstract

We calculate the threshold singularities in one-dimensional models using the universal low-energy formfactors obtained in the framework of the non-linear Luttinger liquid model. We find the reason why the simplified picture of the impurity moving in the Luttinger liquid leads to the correct results. We obtain the prefactors of the singularities including their $k$- dependence at small $k<<p_F$.