====== Theory of spectroscopy, dynamics and numerical methods for complex materials ======

===== Research =====

The main body of the research activities in our group is aimed at advancing the fundamental understanding of many body quantum materials. We not only focuses on the description of the groundstate of these systems, but also treat the dynamical properties and excitations. We focus on extending our capabilities of performing quantitative calculations of excitations by light ranging from terahertz to x-ray spectroscopy. The calculations are done for bulk crystals, (topological) surfaces, interfaces, thin films, impurity centres, or the active centres in many of the known enzymes and catalysts.  Of particular interest are the interaction between local entangled electronic states and multiplets as one sees in transition metal and rare earth centers interacting with delocalized states. Often such systems possess a large number of low energy electronic degrees of freedom, which are responsible for their rich physical behavior. This behavior does not only make these materials interesting, it also makes them involved to understand. In our group we use a manifold of different methods. The optical response is calculated by solving Maxwell’s equations with possible non-linear response functions. For the electronic description we use methods ranging from density functional theory, which allows one to describe the less correlated systems, to ligand field theory, dynamical mean field theory and exact diagonalization of finite clusters which are applicable to strongly correlated materials. It is an essential aim to introduce chemical realism in the description by developing realistic model Hamiltonians, e.g. by using basis sets of Wannier functions derived from DFT calculations.
Our ultimate goal is to create an ab initio method that can predict the electronic, magnetic and optical (from terahertz to x-rays) response as well as the dynamics of complex quantum materials with variable amount of correlations. We achieve this goal by combining several different levels of theory as indicated above.

In particular, the understanding of these materials and their spectroscopic properties is achieved by focusing on two separate topics:

We work on the further development and the theoretical understanding of new experimental methods related to pump-probe experiments, multi color and non-linear absorption. We focus on spectroscopy techniques from tera-herz to free electron laser and synchrotron based x-ray spectroscopy, both in the frequency and time domain.
We use, develop and implement theoretical methods to calculate optical, magnetic and electronic properties of transition metal and rare earth compounds using mean field, density functional and many-body theory.


==== 1. Theory of dynamics and spectroscopy ====

Spectroscopy in its widest form, including pump-probe experiments, multi color spectroscopy, tera herz, free electron laser, and  synchrotron based x-ray spectroscopies can be used to obtain a manifold of information on local and collective properties of materials. These experiments contain for example: bulk-sensitive hard-x-ray photoemission, core-level x-ray absorption, resonant elastic x-ray diffraction, resonant inelastic x-ray scattering and non-resonant inelastic x-ray scattering. One of the main research activities of our group is to improve the understanding of several of these experimental techniques (both in energy and time domain) as well as the development of numerical toolkits to obtain the essential information from spectroscopic experiments.

==== 2. Development of new numerical methods to solve correlated electron systems ====

We develop new numerical methods to treat problems of excitations and dynamics in correlated quantum materials. The explicit inclusion of electronic entanglement allows us to treat multiplets and their interaction with continuum states with an accuracy that would not have been possible only a few years ago. We merge ideas from quantum chemistry and renormalization group theory to obtain optimal basis sets for the problem at hand. Besides direct exact diagonalization for finite systems we use dynamical mean field theory and develop our own codes to solve the impurity problem using the same methods as are used for the diagonalization of finite systems. 

Recently, it has been shown that combining density functional theory with dynamical mean field theory can be a powerful tool to treat excited states as well as strong correlation effects. We use density functional theory programs in order to obtain Wannier orbitals and model parameters. The models used on this basis can vary from local cluster calculations solved within the multiplet ligand field theory to spin models solved with linear spin-wave theory or to cluster dynamical mean field theory.

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