Hilbert space properties of the many-body localization problem: from full ergodicity to multifractality
ORAL
Abstract
In contrast with Anderson localization where a genuine localization is observed in real space, the many-body localization (MBL) problem is much less understood in the Hilbert space, support of the eigenstates. In this work, using exact diagonalization techniques up to L=24 spin-1/2 particles (i.e. Hilbert space of size N=2.7 millions) we address the ergodicity properties in the underlying N-dimensional complex networks spanned by various computational bases. We report fully ergodic eigenstates in the delocalized phase (irrespective of the computational basis), while the MBL regime features a generically (basis-dependent) multifractal behavior, delocalized but non-ergodic. The MBL transition is signaled by a non-universal jump of the multifractal dimensions.
*This work benefited from the support of the project THERMOLOC ANR-16-CE30-0023-02 of the French National Research Agency (ANR) and by the French Programme Investissements d’Avenir under the program ANR-11-IDEX- 0002-02, reference ANR-10-LABX-0037-NEXT. We acknowledge PRACE for awarding access to HLRS’s Hazel Hen computer based in Stuttgart, Germany under grant number 2016153659, as well as the use of HPC resources from CALMIP (grants 2017-P0677 and 2018-P0677) and GENCI (grant x2018050225).
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Presenters
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Nicolas Laflorencie
- CNRS, Université Paul Sabatier, Laboratoire de Physique Théorique, Toulouse