Tan contact and universal high momentum behavior of the fermion propagator in the BCS-BEC crossover

TL;DR

This paper investigates the universal high momentum behavior of the fermion propagator in the BCS-BEC crossover, deriving the Tan contact and employing nonperturbative methods including Schwinger-Dyson equations and Functional Renormalization Group to analyze the system.

Contribution

It introduces a nonperturbative derivation of the high momentum factorization and applies a Functional Renormalization Group approach to compute the Tan contact across the entire crossover.

Findings

Universal high momentum factorization of the fermion self-energy.

Computed Tan contact as a function of interaction parameters.

Numerical results for the contact in the Unitary Fermi gas.

Abstract

We derive the universal high momentum factorization of the fermion self-energy in the BCS-BEC crossover of ultracold atoms using nonperturbative quantum field theoretical methods. This property is then employed to compute the Tan contact as a function of interaction strength, temperature, chemical potential and Fermi momentum. We clarify the mechanism of the factorization from an analysis of the self-consistent Schwinger-Dyson equation for the fermion propagator, and compute the perturbative contact on the BCS and BEC sides within this framework. A Functional Renormalization Group approach is then put forward, which allows to determine the contact over the whole crossover and, in particular, for the Unitary Fermi gas. We present numerical results from an implementation of the Renormalization Group equations within a basic truncation scheme.