Negative sign problem in continuous-time quantum Monte Carlo: optimal choice of single-particle basis for impurity problems

TL;DR

This paper investigates how the choice of single-particle basis affects the negative sign problem in continuous-time quantum Monte Carlo simulations of impurity models, proposing basis optimization to mitigate the issue.

Contribution

It systematically analyzes the impact of basis choice on the sign problem and demonstrates basis optimization can significantly reduce it in impurity QMC simulations.

Findings

Basis choice greatly influences the sign problem severity.

Diagonalizing intracluster hoppings yields bases that reduce the sign problem.

Optimized bases can improve the efficiency of impurity QMC calculations.

Abstract

The negative sign problem in quantum Monte Carlo (QMC) simulations of cluster impurity problems is the major bottleneck in cluster dynamical mean field calculations. In this paper we systematically investigate the dependence of the sign problem on the single-particle basis. We explore both the hybridization-expansion and the interaction-expansion variants of continuous-time QMC for three-site and four-site impurity models with baths that are diagonal in the orbital degrees of freedom. We find that the sign problem in these models can be substantially reduced by using a non-trivial single-particle basis. Such bases can be generated by diagonalizing a subset of the intracluster hoppings.