Continuous-Time Quantum Monte Carlo Method for the Coqblin-Schrieffer Model

TL;DR

This paper introduces a continuous-time quantum Monte Carlo method tailored for the Coqblin-Schrieffer model, effectively handling orbital degeneracy and accurately capturing the Kondo effect without a sign problem.

Contribution

The authors develop a sign-problem-free Monte Carlo algorithm for the Coqblin-Schrieffer model that efficiently manages arbitrary local degrees of freedom and extends to larger N.

Findings

Accurately reproduces the Kondo effect

Demonstrates efficiency for large N

Aligns well with other methods and exact results

Abstract

An impurity solver based on a continuous-time quantum Monte Carlo method is developed for the Coqblin-Schrieffer model. The Monte Carlo simulation does not encounter a sign problem for antiferromagnetic interactions, and accurately reproduces the Kondo effect. Our algorithm can deal with an arbitrary number N of local degrees of freedom, becomes more efficient for larger values of N, and is hence suitable for models with orbital degeneracy. The dynamical susceptibility and the impurity t-matrix are derived with the aid of the Pad\'e approximation for various values of N, and good agreement is found with other methods and available exact results. We point out that the Korringa-Shiba relation needs correction for a finite value of the exchange interaction.