Optimized Jastrow correlations for periodic systems

In the project Optimized Jastrow correlations for periodic systems and application to dynamic properties`` a method is developed, which should improve the description of electronically strongly correlated material. These correlations stem from the interaction of the electrons among each other. Jastrow correlations are a possibility which explicitly takes the spatial correlations of the wave function into account. Starting point is a Kohn-Sham ground state obtained from a density functional theory calculation. In this state electrons are independent of each other. This means that the probability of finding two electrons with opposite spin is approximately the same, regardless of whether they are far apart or close together. This is a rather crude approximation since the Coulomb repulsion acts between two electrons. To improve this Jastrow correlations are introduced. They ensure that the distance between two electrons becomes not too small. The numerical realization of such a wave function for a solid is the main challenge of the project and could so far only be addressed by Monte Carlo calculations. They have the disadvantage that they could not describe e.g. the excitation spectra. But this is necessary to better understand the properties of strongly correlated materials, e.g. superconductivity. In the Project we want to simplify the problem by exploiting symmetry and by use of diagrammatic methods, so that it becomes numerically tractable. These diagrammatic methods are similar to the treatment of Feynman diagrams in quantum field theory. Further the diagrammatic treatment enables the description of excited states. Examples of strongly correlated materials are high temperature superconductors. These materials lose their electrical resistivity below a certain temperature, usually 90K. Despite intensive research, the microscopic mechanism is still not understood. In the project we want to contribute to the enlightenment, by applying the methods which are successful in other strongly correlated systems, e.g. liquid 3-He or nuclear matter (e.g. neutron stars), to electrons in a solid. Further more we want to apply the method to CuO, which is a prime example where the established theory fails in the description of the spectra. The CuO-plains in high temperature superconductors play a decisive role in the emergence of superconductivity, which makes this material particularly interesting.

In everyday life we are surrounded by materials whose function and properties are determined by the electronic excitation spectrum. One of the best known examples is the transparency or color of glass. Many technological developments have also been made possible by understanding the excitation spectrum, e.g. Transistors, LEDs, photovoltaics, etc. We understand the microscopic and quantum mechanical effects so well that we can essentially calculate the excitation spectrum. This means, if you need a specific form of excitation spectrum for a specific application, you can search for suitable materials on the computer. One problem with this is, that existing methods are very expensive and require a lot of computing time. One approach that we followed in the project is that we have solved the difficult part, the correlation effects, in a model system. This result was then used to calculate a real material. A surprising result is that correlation effects tends to depend rather on global properties of the material, e.g. the average electron density, as on local properties, as the density at a certain point. In other words, in order to calculate the correlation effects in a material, it is sufficient to look very roughly at the material, as through a false pair of glasses. The electron density appears to be blurry and you can only determine the average density. We then calculated the correlation effects in this electron mash. (Another advantage is that you can use advanced methods in the model system that are difficult or impossible to realize in the real system.) We then mixed the result with the high-resolution density (the method is called time-dependent density -Functional theory) and thus obtained very good results. Another advantage is that one only has to calculate the correlation effects for the different pulp densities once. Our results are freely accessible and can be used for a variety of materials. However, there is still room for improvement for certain properties in insulators and semiconductors; we continue to pursue the approach and refine it by expanding the range of model systems.