# Soutenance de thèse: Giulio Bertoli

Soutenance de thèse:

*Many-body localization of two-dimensional disordered bosons*

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## Giulio Bertoli

**Jury**:

- Rapporteur :
**Anna Minguzzi**(LPMMC, Grenoble) - Rapporteur :
**Vladimir Yudson**(Russian Quantum Center, Moscow) - Examinateur :
**Vladimir Kravtsov**(ICTP, Trieste) - Examinateur :
**Nicolas Pavloff**(LPTMS, Orsay) - Directeur de thèse :
**Georgy Shlyapnikov**(LPTMS, Orsay)

**Résumé**:

The study of the interplay between localization and interactions in disordered quantum systems led to the discovery of the interesting physics of many-body localization (MBL). This remarkable phenomenon provides a generic mechanism for the breaking of ergodicity in quantum isolated systems, and has stimulated several questions such as the possibility of a finite-temperature fluid-insulator transition. At the same time, the domain of ultracold interacting atoms is a rapidly growing field in the physics of disordered quantum systems.

In this Thesis, we study many-body localization in the context of two-dimensional disordered ultracold bosons. After reviewing some importance concepts, we present a study of the phase diagram of a two-dimensional weakly interacting Bose gas in a random potential at finite temperatures. The system undergoes two finite-temperature transitions: the MBL transition from normal fluid to insulator and the Berezinskii-Kosterlitz-Thouless transition from algebraic superfluid to normal fluid. At T=0, we show the existence of a tricritical point where the three phases coexist. We also discuss the influence of the truncation of the energy distribution function at the trap barrier, a generic phenomenon for ultracold atoms. The truncation limits the growth of the localization length with energy and, in contrast to the thermodynamic limit, the insulator phase is present at any temperature. Finally, we conclude by discussing the stability of the insulating phase with respect to highly energetic particles in systems defined on a continuum.

**Date/Time : ** 05/02/2019 - *14:30 - 17:30*

**Location : ** IPN-batiment 100, Auditoriurm

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