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In this talk, I will give an introduction to the phenomenon of many body localization and its differences from single particle Anderson localization. Then, I discuss our recent exact diagonalization results of the many body localization (MBL) transition in the random field Heisenberg chain and present in particular the energy vs disorder strength phase diagram that was obtained from various estimators. The phase boundary is strongly energy dependent, thus providing evidence for an extensive mobility edge. At low disorder strength, eigentstates are ergodic and can be described by GOE statistics, while in the strong field phase, they are localized and show Poisson statistics. In the MBL phase, the eigenstate thermalization hypothesis is no longer fulfilled. If time permits, I will provide an outlook on our current work, where we look at the exact time evolution of initial product states. Reference: Luitz, D. J., Laflorencie, N. & Alet, F. Many-body localization edge in the random-field Heisenberg chain. Phys. Rev. B 91, 081103 (2015).

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David Luitz, Toulouse
Seminar Room TP 0.03
Contact: Simon Trebst