Functional renormalization group approach to low-energy effective interactions in multi-band many-fermion systems
Final Report Abstract
In this project the so-called constrained functional renormalization group (cfRG) was explored. It is based on the more general functional renormalization group formalism for interacting fermions. It constitutes an extension of the widely-used constrained random phase approximation (cRPA) for the calculation of low-energy effective interactions in multiband electron systems in solids. In the first part of project, we tested a channel-decomposed variant of the cfRG in two twodimensional models. In one model, which was close to graphene, the cfRG corrections to cRPA turned out to be small. In the other model, closer to copper oxide materials, the changes with respect to cRPA were stronger. We also interpreted these changes in physical terms. A particular finding were perturbatively generated antiferromagnetic components in the effective interaction that cannot be found using the cRPA. Stimulated by communications with colleagues working with Quantum Monte Carlo (QMC) methods, we then analyzed other three-band models. In these models, the QMC results pointed to a near-cancellation of the renormalizations of the interactions in the reduction to the target-band effective model. By using the cfRG, we could clarify this effect as being based on an intricate loop cancellation on the right hand side of the cfRG flow equation. The subsequent goal of the collaboration with the QMC colleagues, the QMC solution of a low-energy effective model in which the interactions were computed by the cfRG, was pursued with quite some effort and an extensive interchange of data and codes. Unfortunately, the QMC evaluation of the cfRG effective model turned out to be hampered by a severe sign problem. Within this project, no solution could be found. Instead, we continued to search for reduction of the complexity of the cfRG approach. This lead to a recent manuscript in which suitable approximations for wavevector-, frequency- and orbital dependence of the effective interactions are tested. The application of the simplified schemes allowed us to obtain results with better momentum and frequency resolution. Again, we found various deviations from the cRPA treatment, indicating that the cfRG really adds new relevant physics to the low-energy effective model.
Publications
- Efficient vertex parametrization for the constrained functional renormalization group for effective low-energy interactions in multiband systems
Carsten Honerkamp
- Low-energy effective interactions beyond the constrained random-phase approximation by the functional renormalization group. Phys. Rev. B 92, 045113 (2015)
Michael Kinza and Carsten Honerkamp
(See online at https://doi.org/10.1103/PhysRevB.92.045113)
