# Entropy and Exact Matrix-Product Representation of the Laughlin Wave Function

## Abstract

An analytical expression for the von Neumann entropy of the Laughlin wave function is obtained for any possible bipartition between the particles described by this wave function, for a filling fraction {nu}=1. Also, for a filling fraction {nu}=1/m, where m is an odd integer, an upper bound on this entropy is exhibited. These results yield a bound on the smallest possible size of the matrices for an exact representation of the Laughlin ansatz in terms of a matrix-product state. An analytical matrix-product state representation of this state is proposed in terms of representations of the Clifford algebra. For {nu}=1, this representation is shown to be asymptotically optimal in the limit of a large number of particles.

- Authors:

- Departament d'Estructura i Constituents de la Materia, Universitat de Barcelona, 647 Diagonal, 08028 Barcelona (Spain)
- (Australia)

- Publication Date:

- OSTI Identifier:
- 20955433

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review Letters; Journal Volume: 98; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevLett.98.060402; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CLIFFORD ALGEBRA; ENTROPY; EXACT SOLUTIONS; MATRICES; WAVE FUNCTIONS

### Citation Formats

```
Iblisdir, S., Latorre, J. I., Orus, R., and School of Physical Sciences, University of Queensland, QLD 4072.
```*Entropy and Exact Matrix-Product Representation of the Laughlin Wave Function*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVLETT.98.060402.

```
Iblisdir, S., Latorre, J. I., Orus, R., & School of Physical Sciences, University of Queensland, QLD 4072.
```*Entropy and Exact Matrix-Product Representation of the Laughlin Wave Function*. United States. doi:10.1103/PHYSREVLETT.98.060402.

```
Iblisdir, S., Latorre, J. I., Orus, R., and School of Physical Sciences, University of Queensland, QLD 4072. Fri .
"Entropy and Exact Matrix-Product Representation of the Laughlin Wave Function". United States.
doi:10.1103/PHYSREVLETT.98.060402.
```

```
@article{osti_20955433,
```

title = {Entropy and Exact Matrix-Product Representation of the Laughlin Wave Function},

author = {Iblisdir, S. and Latorre, J. I. and Orus, R. and School of Physical Sciences, University of Queensland, QLD 4072},

abstractNote = {An analytical expression for the von Neumann entropy of the Laughlin wave function is obtained for any possible bipartition between the particles described by this wave function, for a filling fraction {nu}=1. Also, for a filling fraction {nu}=1/m, where m is an odd integer, an upper bound on this entropy is exhibited. These results yield a bound on the smallest possible size of the matrices for an exact representation of the Laughlin ansatz in terms of a matrix-product state. An analytical matrix-product state representation of this state is proposed in terms of representations of the Clifford algebra. For {nu}=1, this representation is shown to be asymptotically optimal in the limit of a large number of particles.},

doi = {10.1103/PHYSREVLETT.98.060402},

journal = {Physical Review Letters},

number = 6,

volume = 98,

place = {United States},

year = {Fri Feb 09 00:00:00 EST 2007},

month = {Fri Feb 09 00:00:00 EST 2007}

}

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