Project covers theoretical/computational studies of exotic phases of quantum matter (especially with fractional and non-Abelian quantum statistics) in graphene and other modern nanomaterials. It is aimed at both fundamental effects and application in future graphene nanotechnology (especially in quantum information technology, via the concept of topological quantum computation). Major goals are: (i) implementing powerful computational methods acquired during the preceding IEF (large scale configuration interaction, quantum Monte Carlo, density functional theory) for application in modelling electronic structure and many-body effects in nanostructures; (ii) understanding new many-body effects in low-dimensional systems (especially those related to emergence of exotic electronic phases), applicable in quantum information technology; (iii) building a research group focused on nanoscience/nanotechnology, benefitting from collaboration with University of Cambridge established during the IEF.Project’s success relies on Applicant’s experience (mostly in fundamental research, but also in teaching and leadership), previous and gained during the preceding IEF, and on superb quality of research groups with whom collaboration has been established during the IEF (Cambridge, Oxford, Penn State).The main results will be: (i) improved understanding of the studied phenomena; (ii) shared collaboration between group at host institution (WrUT) and host of previous IEF (Cambridge), including student/lecturer exchange and joint research.