The Operator Product Expansion Beyond Leading Order for Two-Component Fermions

TL;DR

This paper extends the Operator Product Expansion to include finite range corrections in strongly interacting two-component fermion gases, improving the accuracy of universal relation predictions and momentum distribution analysis.

Contribution

It derives the $1/k^6$ tail correction using OPE, enhancing the understanding of finite range effects beyond leading order in fermionic systems.

Findings

Including the $1/k^6$ correction improves agreement with QMC data.

Finite range effects significantly influence the momentum distribution tail.

The approach clarifies the roles of scattering length and effective range.

Abstract

We consider a homogeneous, balanced gas of strongly interacting fermions in two spin states interacting through a large scattering length. Finite range corrections are needed for a quantitative description of data which experiments and numerical simulations have provided. We use a perturbative field theoretical framework and a tool called the Operator Product Expansion (OPE), which together allow for the expression of finite range corrections to the universal relations and momentum distribution. Using the OPE, we derive the $1/k^6$ part of the momentum tail, which is related to the sum of the derivative of the energy with respect to the finite range and the averaged kinetic energy of opposite spin pairs. By comparing the $1/k^4$ term and the $1/k^6$ correction in the momentum distribution to provided Quantum Monte Carlo (QMC) data, we show that including the $1/k^6$ part offers marked improvements. Our field theoretical approach allows for a clear understanding of the role of the scattering length and finite effective range in the universal relations and the momentum distribution.