Disorder and interactions between particles are common features of most physical systems. What are the possible classes of behaviour that a closed quantum system can have in the presence of both disorder and interactions? Although easy to formulate, this fundamental question of quantum statistical physics remains open.
Most systems in nature reach thermal equilibrium during the course of their evolution because their microscopic dynamics is chaotic. However, this is not the only possibility. Recently, many-body localization  — which arises due to quenched disorder and interactions – has come to attention as a generic mechanism that breaks ergodicity and prevents the system from thermalizing. This is in contrast to Anderson localization and integrable models, which also break ergodicity but in a non-generic way (i.e., they require either an absence of interactions or finely tuned coupling constants).
Many-body localized systems are promising for applications in quantum computing because they are able to “escape” thermalization even at “infinite” temperature. Because of this, their states can retain quantum coherence and are a promising venue to realize quantum order even at high temperature. In this sense, because they avoid dissipation, many-body localized systems can act as protected “quantum memories” for extended periods. Alternatively, many-body localization could boost the stability of topological phases of matter, which are usually fragile and realized only at low temperatures. The exotic non-local correlations in these phases, enhanced by many-body localization, would give another route to constructing protected quantum memory.
The implications of many-body localization are far-reaching: non-ergodic dynamics, the existence of novel phases and phase transitions that are forbidden by traditional statistical mechanics, possibility of designing robust quantum computing schemes, etc. Apart from many exciting theoretical prospects, recent experiments  have detected first evidence of many-body localization in optical lattices, while many other other experiments are currently under way.
Project. The goal of this project is to use quantum information techniques to study properties of many-body localized systems and, more generally, the dynamics of interacting disordered systems far from equilibrium. The project will focus on quantum entanglement in such systems and will include the development of numerical algorithms inspired by entanglement, such as tensor networks . In addition to the theoretical understanding of many-body localized systems, we will identify routes by which complex entanglement structures and their dynamical evolution can be probed and possibly protected from decoherence in experiments. We will also investigate how intricate types of order, like topological order, can be made more robust due to many-body localization.
In the initial phase, we will set up a foundation for the project based on the theoretical progress on many-body localization since 2010. As the toy model, we will focus on the Heisenberg model of spins-1/2 in a random field. We will study the dynamics of entanglement in this model when the system is driven out of equilibrium. The characteristic logarithmic-in-time growth of entanglement will help us arrive at the effective theory of many-body localized phases which was established in 2013. This will allow us to understand some of the universal properties of localized phases that have been observed in experiment . The second goal of the first phase of the project is a numerical implementation of a tensor-network algorithm describing a one-dimensional spin chain (e.g., the transverse-field Ising model). In doing so, we will learn how to study entanglement, dynamics and phase transitions using variational tensor network simulations.