Single-particle spectral density of the unitary Fermi gas: Novel approach based on the operator product expansion, sum rules and the maximum entropy method

TL;DR

This paper introduces a novel approach combining operator product expansion, sum rules, and maximum entropy methods to analyze the single-particle spectral density of the unitary Fermi gas, providing insights into its dispersion and pairing gap.

Contribution

It develops a new framework for extracting spectral densities of the unitary Fermi gas using sum rules and maximum entropy, improving understanding of its quasiparticle properties.

Findings

Spectral densities agree with quantum Monte Carlo results.

Dispersion relations and pairing gaps are extracted.

Method provides a new tool for studying strongly interacting fermions.

Abstract

Making use of the operator product expansion, we derive a general class of sum rules for the imaginary part of the single-particle self-energy of the unitary Fermi gas. The sum rules are analyzed numerically with the help of the maximum entropy method, which allows us to extract the single-particle spectral density as a function of both energy and momentum. These spectral densities contain basic information on the properties of the unitary Fermi gas, such as the dispersion relation and the superfluid pairing gap, for which we obtain reasonable agreement with the available results based on quantum Monte-Carlo simulations.