# On calculation of RKKY range function in one dimension

## TL;DR

This paper addresses the challenge of calculating the RKKY interaction range function in one-dimensional electron gases, focusing on handling and avoiding strong singularities in the perturbation theory.

## Contribution

It introduces a method to manage and circumvent singularities in the RKKY range function calculation for 1D systems, advancing theoretical understanding.

## Key findings

- Presented a new approach to handle singularities in 1D RKKY calculations
- Proposed a method to avoid singularities in perturbation theory
- Enhanced the theoretical framework for 1D RKKY interactions

## Abstract

The effect of strong singularity in the calculation of range function for the RKKY interaction in 1D electron gas is discussed. The method of handling this singularity is presented. A possible way of avoiding the singularity in the Ruderman-Kittel perturbation theory in 1D is described.