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.
@article{arxiv.1906.00880,
title = {Symmetric Improved Estimators for Continuous-time Quantum Monte Carlo},
author = {Josef Kaufmann and Patrik Gunacker and Alexander Kowalski and Giorgio Sangiovanni and Karsten Held},
journal= {arXiv preprint arXiv:1906.00880},
year = {2019}
}