Signatures of many-body localization in the dynamics of two-level systems in glasses

We study the dynamics and the spread of entanglement of two-level systems (TLSs) in amorphous solids at low temperatures (around 1K). By considering the coupling to phonons within the framework of the Lindblad equation, we show that the wide distribution of disorder leads to all sorts slow dynamics for the TLSs, that can be interpreted within the theory of many-body localization (MBL). In particular, we show that the power-law decay of the concurrence, which is typical of MBL isolated systems, survives the coupling to phonons in a wide region of parameter space. We discuss the relevance and implications for experiments.