Continuous-time Monte Carlo methods for quantum impurity models

TL;DR

This paper reviews continuous-time quantum Monte Carlo algorithms for solving quantum impurity models, which are crucial in nanoscience and correlated electron systems, providing detailed derivations, strengths, weaknesses, and future prospects.

Contribution

It offers a comprehensive review and detailed derivations of continuous-time Monte Carlo algorithms tailored for quantum impurity models, facilitating implementation and application.

Findings

Algorithms effectively access high and low energy scales

Successfully applied to various physically realistic models

Discusses strengths, weaknesses, and future directions

Abstract

Quantum impurity models describe an atom or molecule embedded in a host material with which it can exchange electrons. They are basic to nanoscience as representations of quantum dots and molecular conductors and play an increasingly important role in the theory of "correlated electron" materials as auxiliary problems whose solution gives the "dynamical mean field" approximation to the self energy and local correlation functions. These applications require a method of solution which provides access to both high and low energy scales and is effective for wide classes of physically realistic models. The continuous-time quantum Monte Carlo algorithms reviewed in this article meet this challenge. We present derivations and descriptions of the algorithms in enough detail to allow other workers to write their own implementations, discuss the strengths and weaknesses of the methods, summarize the problems to which the new methods have been successfully applied and outline prospects for future applications.