From weak to strong: constrained extrapolation of perturbation series with applications to dilute Fermi systems

TL;DR

This paper introduces a novel extrapolation method for perturbation series constrained by strong-coupling data, effectively extending their validity into nonperturbative regimes, with successful applications to dilute Fermi gases.

Contribution

The authors develop a new truncation-order-dependent re-expansion technique constrained by strong-coupling information, outperforming traditional methods like Padé and Borel extrapolations.

Findings

Method outperforms Padé and Borel extrapolations.

Results for 3D Fermi gas match quantum Monte Carlo data.

Robust ground-state energy estimates across regimes.

Abstract

We develop a method that uses truncation-order-dependent re-expansions constrained by generic strong-coupling information to extrapolate perturbation series to the nonperturbative regime. The method is first benchmarked against a zero-dimensional model field theory and then applied to the dilute Fermi gas in one and three dimensions. Overall, our method significantly outperforms Pad\'e and Borel extrapolations in these examples. The results for the ground-state energy of the three-dimensional Fermi gas are robust with respect to changes of the form of the re-expansion and compare well with quantum Monte Carlo simulations throughout the BCS regime and beyond.