Disordered and strongly-correlated systems: a new theoretical approach
A primary tool to understand the properties of matter is Density Functional Theory (DFT), a reformulation of the many-electron Schroedinger equation based on a functional of the electronic density (rather than the wave-function). Although such formulation is in principle exact, its practical implementation has to rely on approximations, which, despite being successful in explaining many properties of complex molecules and condensed matter, fail when correlation among electrons becomes important.
In recent years, the hosting group has developed a formalism to deal with strong correlation in density functional theory, based on the exact DFT limit of infinite coupling strength. The formalism has also been extended to bosonic systems with different kind of long-ranged repulsive interactions with very promising proof of principle results. The underlying fixed point equations that need to be solved are non-standard and very little work on the numerical side (with the exception of primitive proof of principle implementations) has been done so far.
The researcher in this project is an applied mathematician with outstanding track record in designing numerical algorithms for several different physical problems. In particular, he has developed a new method to solve the non-linear Schroedinger one-particle equations, called spectral renormalization method, which is the perfect tool to solve the fixed point problem related to the strong-coupling limit of DFT.
In this project we will put together the expertise of the researcher and of the host to bring to full maturity the new theoretical framework of DFT for strongly-correlated systems. In particular, we plan to apply the new methodology to study systems with disorder, analyzing Anderson localization in the presence of strong correlation.