Duality of reduced density matrices and their eigenvalues

Abstract

For states of quantum systems of $N$ particles with harmonic interactions we prove that each reduced density matrix $\rho$ obeys a duality condition. This condition implies duality relations for the eigenvalues ${\lambda }_k$ of $\rho$ and relates a harmonic model with length scales $l_1,l_2,\dots ,l_N$ with another one with inverse lengths $1/l_1,1/l_2,\dots ,1/l_N$. Entanglement entropies and correlation functions inherit duality from $\rho$. Self-duality can only occur for noninteracting particles in an isotropic harmonic trap.

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Cited by in corpus (4)

• Number-parity effect for confined fermions in one dimension
• Pinning of Fermionic Occupation Numbers: General Concepts and One Dimension
• Influence of the Fermionic Exchange Symmetry beyond Pauli's Exclusion Principle
• Pinning of fermionic occupation numbers: Higher spatial dimensions and spin