Delocalized Glassy Dynamics and Many Body Localization

Giulio Biroli (1, 2) , Marco Tarzia (3)

1 LPS - Laboratoire de Physique Statistique de l'ENS
2 IPHT - Institut de Physique Théorique - UMR CNRS 3681
3 LPTMC - Laboratoire de Physique Théorique de la Matière Condensée

We analyze the unusual slow dynamics that emerges in the bad metal delocalized phase preceding the Many-Body Localization transition by using single-particle Anderson Localization on the Bethe lattice as a toy model of many-body dynamics in Fock space. We probe the dynamical evolution by measuring observables such as the imbalance and equilibrium correlation functions, which display slow dynamics and power-laws strikingly similar to the ones observed in recent simulations and experiments. We relate this unusual behavior to the non-ergodic spectral statistics found on Bethe lattices. We discuss different scenarii, such as a true intermediate phase which persists in the thermodynamic limit versus a glassy regime established on finite but very large time and length-scales only, and their implications for real space dynamical properties. In the latter, slow dynamics and power-laws extend on a very large time-window but are eventually cut-off on a time-scale that diverges at the MBL transition.

Domaines: Mécanique statistique [cond-mat.stat-mech]; Physique Quantique [quant-ph]

Giulio Biroli, Marco Tarzia. Delocalized Glassy Dynamics and Many Body Localization. 2017. ⟨cea-01547373⟩