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In this talk I will discuss how entanglement and the eigenstates (natural orbitals) and eigenvalues (occupations) of the one-particle density matrix can be used to characterize the many-body localization transition and phases. Many-body localization is the interacting version of the Anderson insulator, and is reflected both as localization of particles in real space, as well as in Fock-space. The study of entanglement, both in eigenstates and its evolution after quenches, has been instrumental in advancing our understanding of many-body localized phases. The entanglement entropy of eigenstates goes from an area law in the localized phase, reflecting the real space localization of wave functions, to an volume law in the delocalized phase, with diverging fluctuations at the transition. In contrast, a global quench within the many-body localized phase gives rise to a slowly (logarithmically) increasing entanglement entropy. The entropy of occupations in the one-particle density matrix turns out to have similar properties as the entanglement entropy--area law in localized phase, volume law in delocalized phase, and diverging fluctuations at the transition--but this is reflecting the Fock space structure of the eigenstates. Finally, the inverse participation ratio of the natural orbitals can be used to define a one-particle localization length in the localized phase.

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Jens Bardason, MPI-PKS Dresden
Seminar Room TP 0.03
Contact: not specified