# Ground state of hard-core bosons in one-dimensional periodic potentials

## Abstract

With Girardeau's Fermi-Bose mapping, we find the exact ground states of hard-core bosons residing in a one-dimensional periodic potential. The analysis of these ground states shows that when the number of bosons N is commensurate with the number of wells M in the periodic potential, the boson system is a Mott insulator whose energy gap, however, is given by the single-particle band gap of the periodic potential; when N is not commensurate with M, the system is a metal (not a superfluid). In fact, we argue that there may be no superfluid phase for any one-dimensional boson system in terms of Landau's criterion of superfluidity. The Kronig-Penney potential is used to illustrate our results.

- Authors:

- Institute of Physics, Chinese Academy of Sciences, Beijing 100080 (China)

- Publication Date:

- OSTI Identifier:
- 20982164

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.75.023613; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; BOSONS; ENERGY GAP; FERMIONS; GROUND STATES; METALS; ONE-DIMENSIONAL CALCULATIONS; PARTICLES; PERIODICITY; POTENTIALS; SUPERFLUIDITY

### Citation Formats

```
Lin, Yuan, and Wu, Biao.
```*Ground state of hard-core bosons in one-dimensional periodic potentials*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.023613.

```
Lin, Yuan, & Wu, Biao.
```*Ground state of hard-core bosons in one-dimensional periodic potentials*. United States. doi:10.1103/PHYSREVA.75.023613.

```
Lin, Yuan, and Wu, Biao. Thu .
"Ground state of hard-core bosons in one-dimensional periodic potentials". United States.
doi:10.1103/PHYSREVA.75.023613.
```

```
@article{osti_20982164,
```

title = {Ground state of hard-core bosons in one-dimensional periodic potentials},

author = {Lin, Yuan and Wu, Biao},

abstractNote = {With Girardeau's Fermi-Bose mapping, we find the exact ground states of hard-core bosons residing in a one-dimensional periodic potential. The analysis of these ground states shows that when the number of bosons N is commensurate with the number of wells M in the periodic potential, the boson system is a Mott insulator whose energy gap, however, is given by the single-particle band gap of the periodic potential; when N is not commensurate with M, the system is a metal (not a superfluid). In fact, we argue that there may be no superfluid phase for any one-dimensional boson system in terms of Landau's criterion of superfluidity. The Kronig-Penney potential is used to illustrate our results.},

doi = {10.1103/PHYSREVA.75.023613},

journal = {Physical Review. A},

number = 2,

volume = 75,

place = {United States},

year = {Thu Feb 15 00:00:00 EST 2007},

month = {Thu Feb 15 00:00:00 EST 2007}

}

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