On the Infinite Variance Problem in Fermion Models
Abstract
Monte Carlo calculations of fermionic systems with continuous auxiliary fields frequently suffer from a diverging variance. If a system has the infinite variance problem, one cannot estimate observables reliably even with an infinite number of samples. In this paper, we explore a method to deal with this problem based on sampling according to the distribution of a system with an extra time-slice. The necessary reweighting factor is computed both perturbatively and through a secondary Monte Carlo. We show that the Monte Carlo reweigthing coupled to the use of a non-biased estimator of the reweigthing factor leads to a method that eliminates the infinite variance problem at a very small extra cost. We compute the double occupancy in the Hubbard model at half-filling to demonstrate the method and compare the results to well established results obtained by other methods.
Cite
@article{arxiv.2211.06419,
title = {On the Infinite Variance Problem in Fermion Models},
author = {Andrei Alexandru and Paulo Bedaque and Andrea Carosso and Hyunwoo Oh},
journal= {arXiv preprint arXiv:2211.06419},
year = {2023}
}
Comments
9 pages, 4 figures