A solution for infinite variance problem of fermionic observables

Abstract

Fermionic Monte Carlo calculations with continuous auxiliary fields often encounter infinite variance problem from fermionic observables. This issue renders the estimation of observables unreliable, even with an infinite number of samples. In this work, we show that the infinite variance problem stems from the fermionic determinant. Also, we propose an approach to address this problem by employing a reweighting method that utilizes the distribution from an extra time-slice. Two strategies to compute the reweighting factor are explored: one involves truncating and analytically calculating the reweighting factor, while the other employs a secondary Monte Carlo estimation. With Hubbard model as a testbed, we demonstrate that utilizing the sub-Monte Carlo estimation, coupled with an unbiased estimator, offers a solution that effectively mitigates the infinite variance problem at a minimal additional cost.

Comments: 7 pages, 3 figures, Proceedings of the 40th International Symposium on Lattice Field Theory (Lattice 2023), July 31st - August 4th, 2023, Fermi National Accelerator Laboratory