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

## 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.

- Authors:

- ECT*, Villa Tambosi, 38123 Villazzano (Trento) (Italy)
- (Japan)
- Department of Physics, Keio University, Yokohama 223-8522 (Japan)
- RIKEN Nishina Center, Wako, Saitama 351-0198 (Japan)
- Department of Physics, Tokyo Institute of Technology, Meguro, Tokyo 152-8551 (Japan)

- Publication Date:

- OSTI Identifier:
- 22451176

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics; Journal Volume: 356; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPUTERIZED SIMULATION; ENTROPY; FERMI GAS; MONTE CARLO METHOD; OPERATOR PRODUCT EXPANSION; SELF-ENERGY; SPECTRAL DENSITY; SUM RULES; SUPERFLUIDITY

### Citation Formats

```
Gubler, Philipp, E-mail: pgubler@riken.jp, RIKEN Nishina Center, Wako, Saitama 351-0198, Yamamoto, Naoki, Hatsuda, Tetsuo, RIKEN iTHES Research Group, Wako, Saitama 351-0198, and Nishida, Yusuke.
```*Single-particle spectral density of the unitary Fermi gas: Novel approach based on the operator product expansion, sum rules and the maximum entropy method*. United States: N. p., 2015.
Web. doi:10.1016/J.AOP.2015.03.007.

```
Gubler, Philipp, E-mail: pgubler@riken.jp, RIKEN Nishina Center, Wako, Saitama 351-0198, Yamamoto, Naoki, Hatsuda, Tetsuo, RIKEN iTHES Research Group, Wako, Saitama 351-0198, & Nishida, Yusuke.
```*Single-particle spectral density of the unitary Fermi gas: Novel approach based on the operator product expansion, sum rules and the maximum entropy method*. United States. doi:10.1016/J.AOP.2015.03.007.

```
Gubler, Philipp, E-mail: pgubler@riken.jp, RIKEN Nishina Center, Wako, Saitama 351-0198, Yamamoto, Naoki, Hatsuda, Tetsuo, RIKEN iTHES Research Group, Wako, Saitama 351-0198, and Nishida, Yusuke. Fri .
"Single-particle spectral density of the unitary Fermi gas: Novel approach based on the operator product expansion, sum rules and the maximum entropy method". United States. doi:10.1016/J.AOP.2015.03.007.
```

```
@article{osti_22451176,
```

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

author = {Gubler, Philipp, E-mail: pgubler@riken.jp and RIKEN Nishina Center, Wako, Saitama 351-0198 and Yamamoto, Naoki and Hatsuda, Tetsuo and RIKEN iTHES Research Group, Wako, Saitama 351-0198 and Nishida, Yusuke},

abstractNote = {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.},

doi = {10.1016/J.AOP.2015.03.007},

journal = {Annals of Physics},

number = ,

volume = 356,

place = {United States},

year = {Fri May 15 00:00:00 EDT 2015},

month = {Fri May 15 00:00:00 EDT 2015}

}

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