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

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.

13 pages, 7 figure, 4 tables, Eqs.(13), (15), and (59) are corrected with an additional term called C', published version

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• Non-Universal and Universal Aspects of The Large Scattering Length Limit
• Universal relations for spin-orbit coupled Fermi gas near an s-wave resonance
• Universal relations and normal-state properties of a Fermi gas with laser-dressed mixed-partial-wave interactions
• Universal relations for hybridized $s$- and $p$-wave interactions from spin-orbital coupling
• Large-momentun tail of one-dimensional Fermi gases with spin-orbit coupling
• Local manipulation of quantum magnetism in 1D ultracold Fermi gases across narrow resonances
• Systematic study of large-momentum distribution in nuclei with the operator product expansion