Quantum coherence in the ergodic and many-body localized phase

We use quantum coherence as a tool to study the structure of the eigenstates of disordered and interacting quantum many body systems. In particular, we numerically calculate several different measures of quantum coherence for the excited eigenstates to be able to capture the signatures of the ergodic and the many-body localized phase in these finite systems. It is apparent that the different measures of coherence show different behaviour with the increasing disorder strength. We also investigate how the unitary evolution affects quantum coherence in several disordered spin chains. Starting from a maximal coherent state in the computational basis, we study the dynamics of decoherence in both the ergodic and the many-body localized phase. We show that coherence can capture many important features of quantum dynamical phases and offers important computational advantages.