Research Projects

The concept of strongly correlated flat bands in materials, where electrons are independent of momentum, has been known for a long time. These bands are achieved through the use of ultra cold atomic gases, photonic lattices, and coordination polymers, which provide unprecedented control over the electronic band structure and properties of the material. Engineering quantum systems with customizable flat bands is a current focus of quantum many body research. However, a proper theoretical framework to understand and engineer such materials remains lacking. The coexistence of competing quantum correlations in complex lattice structures and the presence of flat bands complicates the formulation of a theoretical framework. This project aims to construct and implement a suitable theoretical formalism for flat band quantum systems using complementary numerical and analytic techniques. The first part focuses on setting up a non-perturbative numerical scheme for lattice fermion models, which accounts for strong correlation effects in large lattice sizes, accesses the interplay of short-range fluctuations, and captures the properties of experimentally relevant materials. The second part focuses on applying the scheme to numerically engineer and investigate the response of flat band quantum materials to external perturbations, such as strain engineering and disorder. The results of these calculations are expected to serve as benchmarks and open up avenues for future experimental investigations. The final part aims to develop an analytic handle on the physics of flat bands, using a suitable field theory like Landau-Ginzburg-Wilson theory.