# Operator product expansion beyond leading order for two-component fermions

## Abstract

Here, 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. By 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 enables for a clear understanding of the role of the scattering length and finite effective range in the universal relations and the momentum distribution.

- Authors:

- Univ. of Tennessee, Knoxville, TN (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Univ. of Tennessee, Knoxville, TN (United States) ; Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

- OSTI Identifier:
- 1564233

- Alternate Identifier(s):
- OSTI ID: 1328512

- Grant/Contract Number:
- [AC05-00OR22725; AC52-06NA25396]

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review A

- Additional Journal Information:
- [ Journal Volume: 94; Journal Issue: 4]; Journal ID: ISSN 2469-9926

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS

### Citation Formats

```
Emmons, Samuel B., Kang, Daekyoung, and Platter, Lucas. Operator product expansion beyond leading order for two-component fermions. United States: N. p., 2016.
Web. doi:10.1103/PhysRevA.94.043615.
```

```
Emmons, Samuel B., Kang, Daekyoung, & Platter, Lucas. Operator product expansion beyond leading order for two-component fermions. United States. doi:10.1103/PhysRevA.94.043615.
```

```
Emmons, Samuel B., Kang, Daekyoung, and Platter, Lucas. Mon .
"Operator product expansion beyond leading order for two-component fermions". United States. doi:10.1103/PhysRevA.94.043615. https://www.osti.gov/servlets/purl/1564233.
```

```
@article{osti_1564233,
```

title = {Operator product expansion beyond leading order for two-component fermions},

author = {Emmons, Samuel B. and Kang, Daekyoung and Platter, Lucas},

abstractNote = {Here, 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. By using the OPE, we derive the 1/k6 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/k4 term and the 1/k6 correction in the momentum distribution to provided quantum Monte Carlo (QMC) data, we show that including the 1/k6 part offers marked improvements. Our field-theoretical approach enables for a clear understanding of the role of the scattering length and finite effective range in the universal relations and the momentum distribution.},

doi = {10.1103/PhysRevA.94.043615},

journal = {Physical Review A},

number = [4],

volume = [94],

place = {United States},

year = {2016},

month = {10}

}

*Citation information provided by*

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Web of Science

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*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*