A Multi-level Algorithm for Quantum-impurity Models

TL;DR

This paper introduces a continuous-time quantum Monte Carlo algorithm with a multi-level approach for simulating quantum impurity models, improving efficiency and enabling exploration of the sign problem.

Contribution

The paper presents a novel multi-level algorithm that enhances quantum Monte Carlo simulations of impurity models and addresses the sign problem.

Findings

Efficient simulation of the Anderson impurity model without time discretization errors.

The multi-level algorithm generates exponentially many configurations with polynomial effort.

Configurations with positive signs dominate at low temperatures, mitigating the sign problem.

Abstract

A continuous-time path integral Quantum Monte Carlo method using the directed-loop algorithm is developed to simulate the Anderson single-impurity model in the occupation number basis. Although the method suffers from a sign problem at low temperatures, the new algorithm has many advantages over conventional algorithms. For example, the model can be easily simulated in the Kondo limit without time discretization errors. Further, many observables including the impurity susceptibility and a variety of fermionic observables can be calculated efficiently. Finally the new approach allows us to explore a general technique, called the multi-level algorithm, to solve the sign problem. We find that the multi-level algorithm is able to generate an exponentially large number of configurations with an effort that grows as a polynomial in inverse temperature such that configurations with a positive sign dominate over those with negative signs. Our algorithm can be easily generalized to other multi-impurity problems.