25/01/2024: Amirali Hannani @ UniMi

Thursday, January 25, 2024 - 11:15
Sala di Rappresentanza
Dipartimento di Matematica
Università degli Studi di Milano
Via Cesare Saldini 50

SPEAKER: Amirali Hannani (KU Leuven)

Localization and Poisson statistics in the “avalanche model”

The “avalanche model” aka “quantum sun model” has been introduced as a toy model to study the stability of the MBL (Many-body localized) phase. Strong numerical and theoretical heuristics suggest a localization-delocalization transition in this family of models varying a natural parameter $\alpha$. We prove localization (in the many-body sense) and Poisson statistics for this model given $\alpha$ sufficiently small. In this talk, first I give some general preliminaries about MBL (Many-body localization) which motivate the above-mentioned model. Then I introduce the model and recall certain numerical “facts” about the localized phase. Finally, I state our theorem concerning localization and Poisson statistics and give some ideas about the proof which rests on showing certain weak information about the absence of level-attractions in this model. This is a joint work with Wojciech De Roeck (KU Leuven).