# Many-body localization

The phenomenon of many-body localisation received a lot of attention recently, both for its implications in condensed-matter physics of allowing systems to be an insulator even at non-zero temperature as well as in the context of the foundations of quantum statistical mechanics, providing examples of systems showing the absence of thermalisation following out-of-equilibrium dynamics. However, many aspects and features of this phenomenon are far from being well understood, and there is not even agreement in the literature on what the actually defining feature is. We investigate several features and ramifications of this phenomenon: We are concerned with mathematical equivalences between various readings of the phenomenon. We numerically study natural condensed-matter systems and investigate experimentally accessible probes.

**Selected group publications**

- Many-body localisation implies that eigenvectors are matrix-product states

Physical Review Letters 114, 170505 (2015) - Total correlations of the diagonal ensemble herald the many-body localization transition

Physical Review B 92, 180202(R) (2015) - Local constants of motion imply information propagation

New Journal of Physics 17, 113054 (2015) - Drude weight fluctuations in many-body localized systems

Physical Review B 94, 201112(R) (2016)

**Group reviews**

- Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems

Reports in Progress in Physics (2016) - Quantum many-body systems out of equilibrium

Nature Physics 11, 124 (2015)