# Extended Bose-Hubbard model with incompressible states at fractional numbers

## Abstract

The Bose-Hubbard model is extended to include nearest- and far-neighbor interactions and is related to the fractional quantum Hall effect (FQHE). Both models may be studied in optical lattices with quantum gases. The ground state is calculated for the extended Bose-Hubbard model with strong repulsive interactions (weak hopping). Incompressible Mott insulator states are found at rational filling fractions compatible with the principal and secondary FQHE filling fractions of the lowest Landau levels observed experimentally. It is discussed to which extent these states at fractional filling survive or undergoes a Mott insulator transition to a superfluid as hopping terms are included.

- Authors:

- Danish Defense Research Establishment, Ryvangsalle' 1, DK-2100 Copenhagen O (Denmark)

- Publication Date:

- OSTI Identifier:
- 20786770

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevA.73.013628; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOSE-EINSTEIN GAS; BOSONS; GROUND STATES; HALL EFFECT; HUBBARD MODEL; SUPERFLUIDITY

### Citation Formats

```
Heiselberg, H.
```*Extended Bose-Hubbard model with incompressible states at fractional numbers*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVA.73.0.

```
Heiselberg, H.
```*Extended Bose-Hubbard model with incompressible states at fractional numbers*. United States. doi:10.1103/PHYSREVA.73.0.

```
Heiselberg, H. Sun .
"Extended Bose-Hubbard model with incompressible states at fractional numbers". United States.
doi:10.1103/PHYSREVA.73.0.
```

```
@article{osti_20786770,
```

title = {Extended Bose-Hubbard model with incompressible states at fractional numbers},

author = {Heiselberg, H.},

abstractNote = {The Bose-Hubbard model is extended to include nearest- and far-neighbor interactions and is related to the fractional quantum Hall effect (FQHE). Both models may be studied in optical lattices with quantum gases. The ground state is calculated for the extended Bose-Hubbard model with strong repulsive interactions (weak hopping). Incompressible Mott insulator states are found at rational filling fractions compatible with the principal and secondary FQHE filling fractions of the lowest Landau levels observed experimentally. It is discussed to which extent these states at fractional filling survive or undergoes a Mott insulator transition to a superfluid as hopping terms are included.},

doi = {10.1103/PHYSREVA.73.0},

journal = {Physical Review. A},

number = 1,

volume = 73,

place = {United States},

year = {Sun Jan 15 00:00:00 EST 2006},

month = {Sun Jan 15 00:00:00 EST 2006}

}

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