Eigenvalue Distributions of Reduced Density Matrices

This paper discusses a theorem concerning the variational description of the eigenfunctions and eigenvalues of the two complementary reduced density matrices for a many-particle system in a bound state.

Journal of Mathematical PhysicsMar 1, 19674 citations

Properties of Reduced Density Matrices

Theoretical chemistryJan 1, 19760 citations

Eigenvalue Distributions of Reduced Density Matrices

Matthias Christandl, Brent Doran, Stavros Kousidis, Michael Walter

Published Nov 1, 2014• 37 citations

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Abstract

ISSN:1432-0916

DOI: 10.3929/ethz-b-000087827

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Usually, variational calculations for the second-order reduced density matrix are performed subject to the constraint that the `` $P$ '' and `` $Q$ '' matrices are positive semidefinite, which only constrains the lowest eigenvalue of these matrices. We characterize the highest eigenvalue of these matrices and discuss how the associated constraint (which is related to the ground-state energy of the Hamiltonians $H=\ensuremath{-}P$ and $H=\ensuremath{-}Q$) can be implemented in practical calculations. This necessary condition for $N$ -representability should help ensure that the second-order reduced density matrix is not ``overcorrelated.''Usually, variational calculations for the second-order reduced density matrix are performed subject to the constraint that the ``$P$'' and ``$Q$'' matrices are positive semidefinite, which only constrains the lowest eigenvalue of these matrices. We characterize the highest eigenvalue of these matrices and discuss how the associated constraint (which is related to the ground-state energy of the Hamiltonians $H=\ensuremath{-}P$ and $H=\ensuremath{-}Q$) can be implemented in practical calculations. This necessary condition for $N$-representability should help ensure that the second-order reduced density matrix is not ``overcorrelated.''

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Variational Theorem for Reduced Density Matrices

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Journal of Mathematical PhysicsMar 1, 19674 citations

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Theoretical chemistryJan 1, 19760 citations

Usually, variational calculations for the second-order reduced density matrix are performed subject to the constraint that the ``

P

'' and ``

Q

'' matrices are positive semidefinite, which only constrains the lowest eigenvalue of these matrices. We characterize the highest eigenvalue of these matrices and discuss how the associated constraint (which is related to the ground-state energy of the Hamiltonians $H=\ensuremath{-}P$ and $H=\ensuremath{-}Q$) can be implemented in practical calculations. This necessary condition for

N

-representability should help ensure that the second-order reduced density matrix is not ``overcorrelated.''