Aspects of Entanglement in Quantum Many-Body Systems

John W. Clark, Hessam Habibian, Aikaterini D. Mandilara, Manfred L. Ristig

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    Abstract

    Knowledge of the entanglement properties of the wave functions commonly used to describe quantum many-particle systems can enhance our understanding of their correlation structure and provide new insights into quantum phase transitions that are observed experimentally or predicted theoretically. To illustrate this theme, we first examine the bipartite entanglement contained in the wave functions generated by microscopic many-body theory for the transverse Ising model, a system of Pauli spins on a lattice that exhibits an order-disorder magnetic quantum phase transition under variation of the coupling parameter. Results for the single-site entanglement and measures of two-site bipartite entanglement are obtained for optimal wave functions of Jastrow-Hartree type. Second, we address the nature of bipartite and tripartite entanglement of spins in the ground state of the noninteracting Fermi gas, through analysis of its two- and three-fermion reduced density matrices. The presence of genuine tripartite entanglement is established and characterized by implementation of suitable entanglement witnesses and stabilizer operators. We close with a broader discussion of the relationships between the entanglement properties of strongly interacting systems of identical quantum particles and the dynamical and statistical correlations entering their wave functions. © 2010 Springer Science+Business Media, LLC.
    Original languageEnglish
    Pages (from-to)1200-1220
    JournalFoundations of Physics
    Volume40
    Issue number9
    DOIs
    Publication statusPublished - 10 Jun 2010

    Keywords

    • Entanglement measures
    • Free Fermi gas
    • Jastrow-Hartree wave function
    • Quantum phase transitions
    • Transverse Ising model
    • Tripartite entanglement

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