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Reduced Density Matrix of Permutational Invariant Many-body Systems

Reduced Density Matrix of Permutational Invariant Many-body Systems We consider density matrices which are sums of projectors on states spanning irreducible representations of the permutation group of L sites (eigenstates of permutational invariant quantum system with L sites) and construct reduced density matrix ρ n for blocks of size n<L by tracing out L−n sites, viewed as environment. Explicit analytic expressions of the elements of ρ n are given in the natural basis and the corresponding spectrum of the reduced density matrix is derived. Results apply to other quantum many-body systems with permutational symmetry. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Reduced Density Matrix of Permutational Invariant Many-body Systems

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References (27)

Publisher
Springer Journals
Copyright
Copyright © 2010 by Springer Science+Business Media B.V.
Subject
Mathematics; Computer Science, general; Mathematics, general; Mechanics; Statistical Physics, Dynamical Systems and Complexity; Theoretical, Mathematical and Computational Physics
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-010-9585-3
Publisher site
See Article on Publisher Site

Abstract

We consider density matrices which are sums of projectors on states spanning irreducible representations of the permutation group of L sites (eigenstates of permutational invariant quantum system with L sites) and construct reduced density matrix ρ n for blocks of size n<L by tracing out L−n sites, viewed as environment. Explicit analytic expressions of the elements of ρ n are given in the natural basis and the corresponding spectrum of the reduced density matrix is derived. Results apply to other quantum many-body systems with permutational symmetry.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Sep 17, 2010

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