Spectral functions of the strongly interacting 3D Fermi gas

TL;DR

This paper introduces a real-time computational method for spectral functions of strongly interacting 3D Fermi gases, avoiding ill-posed analytic continuation and providing improved dynamical property predictions.

Contribution

The authors develop a novel real-time approach combining Keldysh path integral with self-consistent T-matrix approximation for direct spectral function calculation.

Findings

Validated method against imaginary time results.

Achieved qualitative improvements over traditional analytic continuation.

Provided insights into the pseudogap regime above T_c.

Abstract

Computing dynamical properties of strongly interacting quantum many-body systems poses a major challenge to theoretical approaches. Usually, one has to resort to numerical analytic continuation of results on imaginary frequencies, which is a mathematically ill-defined procedure. Here, we present an efficient method to compute the spectral functions of the two-component Fermi gas near the strongly interacting unitary limit directly in real frequencies. To this end, we combine the Keldysh path integral that is defined in real time with the self-consistent T-matrix approximation. The latter is known to predict thermodynamic and transport properties in good agreement with experimental observations in ultracold atoms. We validate our method by comparison with thermodynamic quantities obtained from imaginary time calculations and by transforming our real-time propagators to imaginary time. By comparison with state-of-the-art numerical analytic continuation of the imaginary time results, we show that our real-time results give qualitative improvements for dynamical quantities. Moreover, we show that no significant pseudogap regime exists in the self-consistent T-matrix approximation above the critical temperature $T_c$, an issue that has been under significant debate. We close by pointing out the versatile nature of our method as it can be extended to other systems, like the spin- or mass-imbalanced Fermi gas, other Bose-Fermi models, 2D systems as well as systems out of equilibrium.