Frahm Group, Leibniz Universität Hannover
The emphasis of the research is on the investigation of strongly correlated electrons and magnets in reduced spatial dimensions. For studies of the non-perturbative effects of strong quantum fluctuations in such quantum systems exactly solvable models are constructed and analyzed. This work is based on strong experience in the application of sophisticated mathematical techniques such as the Quantum Inverse Scattering Method and the algebraic Bethe Ansatz.
Using these methods the group has studied correlation functions and thermodynamical properties of correlated systems with an emphasis on the effect of their coupling to quantum impurities, i.e. local inhomogeneities with internal degrees of freedom. In addition, quantum field theoretical methods have been used to extract the universal low-energy/low-temperature properties from the exact results obtained for integrable realizations of such systems. Again, a focus of these activities have been applications to quantum impurity problems utilizing, e.g., the strong predictions of (boundary) conformal field theory. The use of these complementary approaches has provided insights into non-trivial manifestations of correlation effects in such problems.
More recently, integrable systems with boundarys which do not conserve particle numbers have been constructed and methods for the analysis of their spectrum have been developped. These are first steps towards studies of the coupling of a correlated system to its environment within a non perturbative approach.