# Correlation effects in superconducting quantum dot systems

## TL;DR

This paper investigates how electron correlations influence a quantum dot coupled to superconductors, using advanced computational methods to compare different theoretical approaches for realistic parameters.

## Contribution

It introduces a comprehensive analysis of correlation effects in superconducting quantum dots using quantum Monte Carlo, perturbation theory, and NRG, highlighting their comparative strengths.

## Key findings

- Correlation effects significantly modify the quantum dot's electronic properties.
- Quantum Monte Carlo provides accurate results for experimentally relevant parameters.
- Comparison reveals strengths and limitations of perturbation theory and NRG.

## Abstract

We study the effect of electron correlations on a system consisting of a single-level quantum dot with local Coulomb interaction attached to two superconducting leads. We use the single-impurity Anderson model with BCS superconducting baths to study the interplay between the proximity induced electron pairing and the local Coulomb interaction. We show how to solve the model using the continuous-time hybridization-expansion quantum Monte Carlo method. The results obtained for experimentally relevant parameters are compared with results of self-consistent second order perturbation theory as well as with the numerical renormalization group method.