Quantum coherence, phases of matter and many-body localization*

Quantum coherence is one of the most fundamental traits of quantum mechanics. The coherence generating power (CGP) is the ability of a quantum unitary map of generating coherence. It is defined as the average coherence produced by the map applied to the set of incoherent states. In this talk I will report upon an unexpected link between these information theoretic concepts, and well known condensed matter quantities. Given two point in the phase diagram of a system one can ask about the CGP of the adiabatic intertwiner connecting the two points. The CGP turns out to be the inverse participation ratio, a quantity used to detect many-body localization (MBL) while for close-by points the CGP is exactly given by the d.c. dielectric polarizability. Using know results we are able to show that, in the thermodynamic limit, the CGP becomes maximal in the ergodic phase and submaximal in the MBL phase while the differential coherence diverges in the ergodic and subdiffusive phase while it tends to a constant in the MBL phase.