# Symmetric Improved Estimators for Continuous-time Quantum Monte Carlo

## TL;DR

This paper introduces symmetric improved estimators for continuous-time quantum Monte Carlo simulations of the multi-orbital Anderson impurity model, significantly reducing noise at high frequencies and enhancing computational accuracy.

## Contribution

It derives new equations of motion for Green's functions using symmetric differentiation, enabling improved estimators that mitigate high-frequency noise in Monte Carlo simulations.

## Key findings

- Reduced noise at large Matsubara frequencies
- Enhanced accuracy of Green's function measurements
- Applicability to multi-orbital Anderson impurity models

## Abstract

We derive equations of motion for Green's functions of the multi-orbital Anderson impurity model by differentiating symmetrically with respect to all time arguments. The resulting equations relate the one- and two-particle Green's function to correlators of up to six particles at four times. As an application we consider continuous-time quantum Monte Carlo simulations in the hybridization expansion, which hitherto suffered from notoriously high noise levels at large Matsubara frequencies. Employing the derived symmetric improved estimators overcomes this problem.