Multifractality as Defining Feature of Many-Body Localisation

Quantum physics often surprises with phenomena that challenge classical intuition. For example, a system of many interacting classical particles, evolving under its own internal dynamics, is known to eventually reach a thermal equilibrium. In the realm of quantum mechanics this is not necessarily true: a single particle, subject to energetic disorder, will refuse to evolve in time and to explore the host system. Rather, due to quantum interference, it will remain spatially confined, leading to a non-thermalising behaviour known as Anderson localisation (AL) [1]. The fate of AL in the presence of many-body interactions, as is the case in any real material, has been an intriguing question for many years. Recent research showed that AL would be robust under the effect of short-range interactions, giving rise to an insulating phase with exactly zero conductivity below a certain critical temperature. The phenomenon was named many-body localisation (MBL) [2]. In the MBL state an isolated quantum system never reaches thermal equilibrium under its own internal dynamics, and thus cannot be described by standard quantum statistical mechanics. This implies that the system retains information about its initial state for arbitrarily long times a quantum information storage potentially very relevant for the development of quantum technology devices.