Aberration of the Green's function estimator in hybridization expansion continuous-time quantum Monte Carlo

TL;DR

This paper identifies a specific bias in the Green's function estimator used in hybridization expansion continuous-time quantum Monte Carlo, caused by Pauli constraints and discrete baths, and discusses potential solutions.

Contribution

It uncovers the origin of the estimator aberration, characterizes affected models, and explains why certain spectra lead to large autocorrelation times.

Findings

The aberration is due to missing Feynman diagrams.

The issue does not occur with worm sampling or continuous baths.

Certain discrete spectra cause large autocorrelation times.

Abstract

We describe an aberration of the resampling estimator for the Green's function customarily used in hybridization expansion continuous-time quantum Monte Carlo. It occurs due to Pauli principle constraints in calculations of Anderson impurity models with baths consisting of a discrete energy spectrum. We identify the missing Feynman diagrams, characterize the affected models and discuss implications as well as solutions. This issue does not occur when using worm sampling or in the presence of continuous baths. However certain energy spectra can be inherently close to a discrete limit, and we explain why autocorrelation times can become very large in these cases.