# Competing orders in one-dimensional half-filled multicomponent fermionic cold atoms: The Haldane-charge conjecture

## Abstract

We investigate the nature of the Mott-insulating phases of half-filled 2N-component fermionic cold atoms loaded into a one-dimensional optical lattice. By means of conformal field theory techniques and large-scale DMRG calculations, we show that the phase diagram strongly depends on the parity of N. First, we single out charged, spin-singlet degrees of freedom that carry a pseudospin S=N/2, making it possible to formulate a Haldane conjecture: For attractive interactions, we establish the emergence of Haldane insulating phases when N is even, whereas a metallic behavior is found when N is odd. We point out that the N=1,2 cases do not have the generic properties of each family. The metallic phase for N odd and larger than 1 has a quasi-long-range singlet pairing ordering with an interesting edge-state structure. Moreover, the properties of the Haldane insulating phases with even N further depend on the parity of N/2. In this respect, within the low-energy approach, we argue that the Haldane phases with N/2 even are not topologically protected but equivalent to a topologically trivial insulating phase and thus confirm the recent conjecture put forward by Pollmann et al.[arXiv:0909.4059 (to be published)].

- Authors:

- Laboratoire de Physique Theorique et Modelisation, CNRS UMR 8089, Universite de Cergy-Pontoise, Site de Saint-Martin, F-95300 Cergy-Pontoise Cedex (France)
- Laboratoire de Physique Theorique, CNRS UMR 5152, Universite Paul Sabatier, F-31062 Toulouse (France)
- Laboratoire de Physique Theorique et Modeles Statistiques, Universite Paris-Sud, CNRS UMR 8626, F-91405 Orsay (France)
- Laboratoire Materiaux et Phenomenes Quantiques, CNRS UMR 7162, Universite Paris Diderot, F-75013 Paris (France)

- Publication Date:

- OSTI Identifier:
- 21596875

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. B, Condensed Matter and Materials Physics

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 12; Other Information: DOI: 10.1103/PhysRevB.84.125123; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1098-0121

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; CONFORMAL INVARIANCE; DEGREES OF FREEDOM; FERMIONS; INTERACTIONS; INTERFERENCE; LASER RADIATION; ONE-DIMENSIONAL CALCULATIONS; PARITY; PHASE DIAGRAMS; QUANTUM FIELD THEORY; SIMULATION; SPIN; STARK EFFECT; ANGULAR MOMENTUM; DIAGRAMS; ELECTROMAGNETIC RADIATION; FIELD THEORIES; INFORMATION; INVARIANCE PRINCIPLES; PARTICLE PROPERTIES; RADIATIONS

### Citation Formats

```
Nonne, H., Lecheminant, P., Capponi, S., Roux, G., and Boulat, E.
```*Competing orders in one-dimensional half-filled multicomponent fermionic cold atoms: The Haldane-charge conjecture*. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVB.84.125123.

```
Nonne, H., Lecheminant, P., Capponi, S., Roux, G., & Boulat, E.
```*Competing orders in one-dimensional half-filled multicomponent fermionic cold atoms: The Haldane-charge conjecture*. United States. doi:10.1103/PHYSREVB.84.125123.

```
Nonne, H., Lecheminant, P., Capponi, S., Roux, G., and Boulat, E. Thu .
"Competing orders in one-dimensional half-filled multicomponent fermionic cold atoms: The Haldane-charge conjecture". United States. doi:10.1103/PHYSREVB.84.125123.
```

```
@article{osti_21596875,
```

title = {Competing orders in one-dimensional half-filled multicomponent fermionic cold atoms: The Haldane-charge conjecture},

author = {Nonne, H. and Lecheminant, P. and Capponi, S. and Roux, G. and Boulat, E.},

abstractNote = {We investigate the nature of the Mott-insulating phases of half-filled 2N-component fermionic cold atoms loaded into a one-dimensional optical lattice. By means of conformal field theory techniques and large-scale DMRG calculations, we show that the phase diagram strongly depends on the parity of N. First, we single out charged, spin-singlet degrees of freedom that carry a pseudospin S=N/2, making it possible to formulate a Haldane conjecture: For attractive interactions, we establish the emergence of Haldane insulating phases when N is even, whereas a metallic behavior is found when N is odd. We point out that the N=1,2 cases do not have the generic properties of each family. The metallic phase for N odd and larger than 1 has a quasi-long-range singlet pairing ordering with an interesting edge-state structure. Moreover, the properties of the Haldane insulating phases with even N further depend on the parity of N/2. In this respect, within the low-energy approach, we argue that the Haldane phases with N/2 even are not topologically protected but equivalent to a topologically trivial insulating phase and thus confirm the recent conjecture put forward by Pollmann et al.[arXiv:0909.4059 (to be published)].},

doi = {10.1103/PHYSREVB.84.125123},

journal = {Physical Review. B, Condensed Matter and Materials Physics},

issn = {1098-0121},

number = 12,

volume = 84,

place = {United States},

year = {2011},

month = {9}

}