Functional renormalization group for fermions in three dimensions

• Applicants: Professor Dr. Carsten Honerkamp; Professor Dr. Manfred Salmhofer
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2015 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 289598096

• Final Report Year: 2021

Final Report Abstract

All in all, the main goal of the project, a workable fRG code for threedimensional correlated electron models, has been achieved. The new code has been tested for the Hubbard model in various variants. More importantly, thanks to the diligent work of several young people, the code and written-up formalism might serve as a platform of a whole body of works in the next years, and might even become a basis for an fRG community code that can also be used by external users without prior fRG experience. Providing this has turned out to be essential over the last few years. While the previous N-patch fRG codes put forward 209 years ago were relatively simple, the necessary and powerful sophistication of the truncated-unity fRG schemes has raised the complexity level for the code development. This is reflected in the observation that a single doctoral student can likely not go the full distance from devising a code, testing and optimizing it and obtaining physically relevant results. We saw this increase development workload in this project, were many of the higher goals (selfenergies, frequency dependence, multi-band models with band crossing points) were only touched upon or left for future work. On the other hand, the project provided a solid basis for future development, both in terms of formalism and in terms of an accessible, scalable code that has shown its use for others already. It also gave birth to additional, very interesting developments with quite some output such as the TU-parquet or the TUfRG-real-space approach.

Publications

• 2018: Truncated unity functional renormalization group for multiband systems with spin-orbit coupling. Frontiers in Physics 6, 32 (2018)
  G. A. H. Schober, J. Ehrlich, T. Reckling, C. Honerkamp
  
• 2018: Truncated-Unity Parquet Equations: Application to the Repulsive Hubbard Model. Phys. Rev. B 98, 075143 (2018)
  C. J. Eckhardt, G. A. H. Schober, J. Ehrlich, C. Honerkamp
  
• 2020: Functional renormalization group for fermion lattice models in three dimensions: application to the Hubbard model on the cubic lattice Phys. Rev. B 102, 195108 (2020)
  J. Ehrlich, C. Honerkamp