This project aims to investigate the role of electron-electron correlations in these systems, with a focus on identifying and characterizing exotic phases such as unconventional superconductivity and various forms of magnetic ordering. Special attention will be given to the combined effects of spin–orbit coupling and electronic interactions, which may stabilize nontrivial phases and lead to novel symmetry-breaking mechanisms.

 

To address these questions, the project will employ a combination of advanced numerical and analytical techniques. Density Matrix Renormalization Group (DMRG) and infinite Projected Entangled Pair States (iPEPS) methods will be used to obtain accurate descriptions of ground-state properties in strongly correlated regimes, while mean-field theory will provide complementary insights and guide the exploration of parameter space.

 

An important aspect of the project is the connection to experimentally realizable systems. Therefore, potential collaborations with experimental groups will be pursued to ensure that theoretical predictions remain relevant and testable, particularly in light of recent advances in engineered graphene structures and spectroscopic probes.

 

Overall, this research aims to deepen our understanding of correlation-driven phenomena in layered graphene systems and contribute to the broader effort of uncovering and controlling novel quantum phases in low-dimensional materials.