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Title: 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:
;  [1];  [1];  [2]
  1. Departament d'Estructura i Constituents de la Materia, Universitat de Barcelona, 647 Diagonal, 08028 Barcelona (Spain)
  2. (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}
}