Continuous-time Quantum Monte Carlo using Worm Sampling

TL;DR

This paper introduces a worm sampling method for continuous-time quantum Monte Carlo simulations that directly samples Green's functions, enhancing efficiency and enabling calculation of complex two-particle Green's functions in quantum many-body systems.

Contribution

The paper develops a worm sampling algorithm for CT-HYB that improves the calculation of general two-particle Green's functions and enhances sampling efficiency near the atomic limit.

Findings

Worm sampling directly measures Green's functions in CT-HYB.

Improves sampling efficiency for two-particle Green's functions.

Enables calculation of off-diagonal susceptibilities and diagrammatic extensions.

Abstract

We present a worm sampling method for calculating one- and two-particle Green's functions using continuous-time quantum Monte Carlo simulations in the hybridization expansion (CT-HYB). Instead of measuring Green's functions by removing hybridization lines from partition function configurations, as in conventional CT-HYB, the worm algorithm directly samples the Green's function. We show that worm sampling is necessary to obtain general two-particle Green's functions which are not of density-density type and that it improves the sampling efficiency when approaching the atomic limit. Such two-particle Green's functions are needed to compute off-diagonal elements of susceptibilities and occur in diagrammatic extensions of the dynamical mean field theory and efficient estimators for the single-particle self-energy.