Thermal correlation functions of the Heisenberg-Ising chain

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The key objective of our research project is the exact and efficient calculation of all thermal correlationfunctions of the one-dimensional Heisenberg model. The Heisenberg model describesthe magnetism of insulators and hence of a large class of technically relevant materialswhich includes, for instance, the high temperature superconductors. Since magnetism is atrue many-body problem, many interesting questions are still open. In particular, we arelacking precise quantitative algorithms for the calculation of experimentally relevantquantities, especially for one- and two-dimensional systems. This is were our projectbegins. The thermal correlation functions we are planning to calculate determine theso-called static structure factor which is measured in neutron scattering experimentsas a functions of temperature and applied magnetic field. So far it can only be approximatelycalculated for very low temperatures. We are expecting that the methods we are goingto develop in our project will be of wider use, e.g., in the framework of the theory of ultra coldgases.