Worm Improved Estimators in Continuous-time Quantum Monte Carlo

TL;DR

This paper introduces improved estimators for continuous-time quantum Monte Carlo, enhancing the accuracy of high-frequency behavior in electronic correlation functions using a worm algorithm, with validation against known models.

Contribution

It develops a general framework for improved estimators in continuous-time QMC and demonstrates their effectiveness for non-density-density interactions.

Findings

Enhanced high-frequency behavior in self-energy and vertex functions

Accurate results for multi-orbital atomic-limit and Falicov-Kimball model

Improved measurement of higher-ordered correlators

Abstract

We derive the improved estimators for general interactions and employ these for the continuous-time quantum Monte Carlo method. Using a worm algorithm we show how measuring higher-ordered correlators leads to an improved high-frequency behavior in irreducible quantities such as the one-particle self-energy or the irreducible two-particle vertex for non-density-density interactions. A good knowledge of the asymptotics of the two-particle vertex is essential for calculating non-local electronic correlations using diagrammatic extensions to the dynamical mean field theory as well as for calculating susceptibilities. We test our algorithm against analytic results for the multi-orbital atomic-limit and the Falicov-Kimball model.