On the Infinite Variance Problem in Fermion Models

TL;DR

This paper introduces a Monte Carlo reweighting method that effectively solves the infinite variance problem in fermionic systems, enabling reliable observable estimation without significant additional computational cost.

Contribution

The authors propose a novel reweighting approach combined with a non-biased estimator to eliminate the infinite variance issue in fermion Monte Carlo simulations.

Findings

Successfully applied to the Hubbard model at half-filling

Eliminates infinite variance with minimal extra cost

Produces results consistent with established methods

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.