Ground-state Properties of Many-body Systems from a Renormalization-Group Approach to Density Functional Theory
Final Report Abstract
It is an exciting era for nuclear physics as we understand better and better the formation of light and medium-mass nuclei based on forces derived from the fundamental theory of the strong interaction. For the calculation of ground-state properties of heavy nuclei, however, Density Functional Theory (DFT) remains to be the method of choice. Based on phenomenologically guided advances, the application of DFT to the nuclear many-body problem has indeed been very successful in recent years and provides us with a universal understanding of ground-state properties of nuclei. Moreover, there have been many conceptional advances aiming directly at ab initio studies of heavy nuclei. The tremendous efforts undertaken in this very active research field are impressively documented by large-scale collaborations, such as the UNEDF/NUCLEI SciDAC collaboration. The present project dealt with a further development of a combination of DFT and socalled Renormalization Group (RG) methods which have been successfully employed to study strongly coupled systems in various research fields in recent years. The use of such RG methods appears to be particularly appealing in the context of DFT as they open up the possibility to connect the energy density functional to the microscopic nuclear forces. In order to guide the further developments of our DFT-RG approach, we applied it to different one-dimensional systems which share at least some aspects with the nuclear many-body problem. Since the convergence of physical observables in terms of the expansion scheme underlying our DFT-RG approach turned out to be very slow, thereby rendering an application of the original formulation of this approach to three-dimensional systems impractical, we proposed a “hybrid approach” which combines conventional Kohn-Sham-DFT with our DFT-RG approach. The resulting new DFT-RG scheme indeed exhibits a significantly faster convergence to the known exact results of the tested models than the original scheme. This new development therefore potentially paves the way for the application of our DFT-RG approach to three-dimensional systems, such as nuclei, in the future.
Publications
- Formation of selfbound states in a one-dimensional nuclear model – a renormalization group based density functional study, J. Phys. G 44, 015101 (2017)
S. Kemler, M. Pospiech, J. Brau
(See online at https://doi.org/10.1088/0954-3899/44/1/015101) - From Microscopic Interactions to Density Functionals, Ph.D. thesis, TU Darmstadt (2017)
S. Kemler
- Surmounting the sign problem in non-relativistic calculations: a case study with massimbalanced fermions, Phys. Rev. D 96, 094506 (2017)
L. Rammelmüller, W. J. Porter, J. E. Drut, J. Braun
(See online at https://doi.org/10.1103/PhysRevD.96.094506)
