Infinite variance problem in fermion models

Monte Carlo calculations of fermionic systems with continuous auxiliary fields frequently suffer from a diverging variance for fermionic observables. If the simulations have an infinite variance problem, one cannot estimate observables reliably even with an arbitrarily large number of samples. In th...

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Bibliographic Details
Published in:Physical review. D 2023-05, Vol.107 (9), Article 094502
Main Authors: Alexandru, Andrei, Bedaque, Paulo F., Carosso, Andrea, Oh, Hyunwoo
Format: Article
Language:English
Subjects:
NUCLEAR PHYSICS AND RADIATION PHYSICS
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Summary:Monte Carlo calculations of fermionic systems with continuous auxiliary fields frequently suffer from a diverging variance for fermionic observables. If the simulations have an infinite variance problem, one cannot estimate observables reliably even with an arbitrarily large number of samples. In this paper, we explore a method to solve this problem using sampling based on 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 reweighting coupled to the use of an unbiased estimator of the reweighting 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.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.107.094502