Laboratoire de Physique Théorique
Toulouse - UMR 5152

The presence of disorder in quantum systems can lead to the striking phenomenon of absence of diffusion and localization, which is stable even in the presence of interactions ; this phenomenon, named (Many-Body) Localization, is a generic way to break thermalization in quantum systems and is characterized by a lot of interesting phenomenology both for fundamental quantum physics (lack of ergodicity, lack of thermalization, emergent integrability, peculiar entanglement behavior, connections to the random matrix theory and so on) and for practical applications (localization as a quantum memory, experimental implementations using optical lattices). I will present two tools which are able to gain insight on the localization transition, one stemming from the idea of ergodicity breaking, which can be detected by a measure of the total correlations in a generic quantum state, and the other dealing with estimating the long-range resonances, through an approximation of the so-called locator expansion. Finally, I will show how subtle correlations in the delocalized phase impair our attempts to investigate the transition with current common numerical methods.