# Threshold singularities in a Fermi gas with attractive potential in one dimension

## Abstract

We consider the one-dimensional gas of fermions with spin S interacting via an attractive δ-function potential using the Bethe *Ansatz* solution. In zero magnetic field the atoms form bound states of N=2S + 1 fermions, i.e. generalized Cooper states with each atom having a different spin component. For low energy excitations the system is a Luttinger liquid and is properly described by a conformal field theory with conformal charge c=1. The linear dispersion of a Luttinger liquid is asymptotically exact in the low-energy limit where the band curvature terms in the dispersion are irrelevant. For higher energy excitations, however, the spectral function displays deviations in the neighborhood of the single-particle (hole) energy, which can be described by an effective X-ray edge type model. Using the Bethe *Ansatz* solution we obtain expressions for the critical exponents for the single-particle (hole) Green’s function. This model can be relevant in the context of ultracold atoms with effective total spin S confined to an elongated optical trap.

- Authors:

- Florida State University, Tallahassee, FL (United States)
- Ukrainian National Academy of Sciences, Kharkov (Ukraine); Max-Planck-Institut für Physik komplexer Systeme, Dresden (Germany)

- Publication Date:

- Research Org.:
- Florida State Univ., Tallahassee, FL (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1228398

- Alternate Identifier(s):
- OSTI ID: 1188312

- Grant/Contract Number:
- FG02-98ER45707; 4-15-13; 0112U007569

- Resource Type:
- Journal Article: Published Article

- Journal Name:
- Nuclear Physics. B

- Additional Journal Information:
- Journal Volume: 892; Journal Issue: C; Journal ID: ISSN 0550-3213

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

### Citation Formats

```
Schlottmann, P., and Zvyagin, A. A.
```*Threshold singularities in a Fermi gas with attractive potential in one dimension*. United States: N. p., 2015.
Web. doi:10.1016/j.nuclphysb.2015.01.009.

```
Schlottmann, P., & Zvyagin, A. A.
```*Threshold singularities in a Fermi gas with attractive potential in one dimension*. United States. doi:10.1016/j.nuclphysb.2015.01.009.

```
Schlottmann, P., and Zvyagin, A. A. Thu .
"Threshold singularities in a Fermi gas with attractive potential in one dimension". United States.
doi:10.1016/j.nuclphysb.2015.01.009.
```

```
@article{osti_1228398,
```

title = {Threshold singularities in a Fermi gas with attractive potential in one dimension},

author = {Schlottmann, P. and Zvyagin, A. A.},

abstractNote = {We consider the one-dimensional gas of fermions with spin S interacting via an attractive δ-function potential using the Bethe Ansatz solution. In zero magnetic field the atoms form bound states of N=2S + 1 fermions, i.e. generalized Cooper states with each atom having a different spin component. For low energy excitations the system is a Luttinger liquid and is properly described by a conformal field theory with conformal charge c=1. The linear dispersion of a Luttinger liquid is asymptotically exact in the low-energy limit where the band curvature terms in the dispersion are irrelevant. For higher energy excitations, however, the spectral function displays deviations in the neighborhood of the single-particle (hole) energy, which can be described by an effective X-ray edge type model. Using the Bethe Ansatz solution we obtain expressions for the critical exponents for the single-particle (hole) Green’s function. This model can be relevant in the context of ultracold atoms with effective total spin S confined to an elongated optical trap.},

doi = {10.1016/j.nuclphysb.2015.01.009},

journal = {Nuclear Physics. B},

number = C,

volume = 892,

place = {United States},

year = {Thu Jan 15 00:00:00 EST 2015},

month = {Thu Jan 15 00:00:00 EST 2015}

}