Resummation of diagrammatic series with zero convergence radius for strongly correlated fermions

TL;DR

This paper presents a method to accurately sum divergent diagrammatic series for strongly correlated fermions, specifically the unitary Fermi gas, using conformal-Borel resummation informed by instanton analysis.

Contribution

It introduces a novel resummation technique combining conformal-Borel transformation with instanton analysis to handle zero convergence radius series in strongly correlated fermionic systems.

Findings

Achieved highly accurate equation of state for the unitary Fermi gas.

Reconciled experimental data with the conjectured fourth virial coefficient.

Demonstrated unbiased results from divergent series in strongly correlated regimes.

Abstract

We demonstrate that summing up series of Feynman diagrams can yield unbiased accurate results for strongly-correlated fermions even when the convergence radius vanishes. We consider the unitary Fermi gas, a model of non-relativistic fermions in three-dimensional continuous space. Diagrams are built from partially-dressed or fully-dressed propagators of single particles and pairs. The series is resummed by a conformal-Borel transformation that incorporates the large-order behavior and the analytic structure in the Borel plane, which are found by the instanton approach. We report highly accurate numerical results for the equation of state in the normal unpolarized regime, and reconcile experimental data with the theoretically conjectured fourth virial coefficient.