Sparse modeling for 2P response and parquet equations

Spintronics, solar energy conversion, energy storage and transmission, quantum computing -- for all these purposes, materials with novel functionalities are asked for. A decisive role in determining the electronic and magnetic properties of a material is played by electrons. As charged particles, they interact with one another through Coulomb interaction. In many cases, despite strong Coulomb repulsion, the electrons can still be viewed as independent particles. In some materials, however, and these are the most intriguing cases, the interaction makes electrons strongly correlated, leading to phenomena that are not easily understood in terms of isolated particles -- they are called emergent -- such as magnetism or superconductivity. To exploit new material properties, theoretical methods that are capable of capturing the effects of strong electronic correlations are needed so that we can understand how emergent phenomena come about. Ideally, we also want to predict the behaviour of materials in response to external perturbations -- magnetic field, light exposure, temperature. Theoretical objects that describe this behaviour are so-called response functions. Their calculation often requires numerical computation of two-particle correlation functions that depend on many variables -- energy, momentum and quantum numbers (such as spin) of two incoming and two outgoing particles. The amount of data needed to directly store two-particle correlation functions is overwhelming even for simple materials and makes the application of advanced quantum field theory methods unfeasible. However, it turns out that this data is highly compressible -- similarly to many images being compressible without significant information loss. In our project we will apply data compression methods, namely sparse modeling, to represent two-particle correlation functions for materials with strongly correlated electrons and compute their properties, such as conductivity, reflectivity or response to magnetic field. The information loss through compression can be quantified and controlled, which makes the computations at the same time feasible and reliable. Building compression into mathematical equations with two-particle correlation functions still however poses a significant challenge. This challenge we will tackle in the project.