# Thermodynamics of Two-impurity Anderson Model with Dzyaloshinskii-Moriya Interaction

## TL;DR

This study uses numerical renormalization group theory to analyze how Dzyaloshinskii-Moriya interaction influences the Kondo temperature in a two-impurity Anderson model, revealing different effects depending on the estimation method and RKKY interaction type.

## Contribution

It provides a comparative analysis of two methods to estimate the Kondo temperature's dependence on Dzyaloshinskii-Moriya interaction, clarifying previous debates.

## Key findings

- Different estimation methods yield linear or quadratic dependence of Kondo temperature on DM interaction.
- Second stage of Kondo screening exponentially depends on DM interaction when RKKY is ferromagnetic.
- Results differ significantly from perturbation theory calculations.

## Abstract

In this work, we use the numerical renormalization group (NRG) theory to study the thermodynamics of the two-impurity Anderson model. Two different methods are used to estimate the effect of the Dzyaloshiskii-Moriya (DM) interaction on the variation of the Kondo temperature. When the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction is vanishing, the two different estimations give different tendency. If we use the peak of the specific heat to identify the variation of the Kondo temperature versus the Dzyaloshiskii-Moriya interaction, we get an almost linear function. However, if we use the low temperature universal curve of the impurity entropy, we get a quadratic function. These results indicate that the previous debates about the influence of the spin-orbit coupling on the Kondo temperature may come from the different definitions of the Kondo temperature. When the RKKY interaction is ferromagnetic, there are two stages of the Kondo screening. Both the two estimations demonstrate that the second stage of the Kondo temperature is exponentially dependent on the DM interaction. There results are dramatically different from those calculated via perturbation theory.