Development of a functional renormalization group to treat interaction effects in strongly disordered electron systems

• Applicant: Professor Dr. Ferdinand Evers
• Subject Area: Experimental Condensed Matter Physics
• Term: from 2012 to 2016
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 198431769

• Final Report Year: 2016

Final Report Abstract

In this project a method ( FRG) has been developed and implemented aiming at improved computations of electronic properties of inhomogenuous systems, such as molecules, atomic clusters and disordered electron films. Building on the functional renormalization group (FRG), the FRG-method includes the interactions between electrons in a perturbative way not unlike present days advanced electronic structure codes (”GW-theory”). The conceptual advantage of FRG over conventional GW-type approaches is that screening effects can be taken into account that tend to escape the GW-methods. Therefore, in principle the FRG has the potential to significantly enhance the numerical accuracy of electronic excitation energies, dielectric responses, transport properties etc. Importantly, it also offers prospects to describe even those ordered electronic phases that are completely out of reach for the standard methods. The price to be paid for harvesting the power of FRG is a high degree of computational complexity. Sophisticated approximation schemes are required, one of which has been devised, implemented and tested in this project, the FRG with an active space approximation. We find that the approach is very promising in terms of computational efficiency (order N 4 scaling with the number of basis functions). Tests for the disordered spinless Hubbard model in 2D indicate that for weak interactions the method is reliable also in terms of accuracy for electronic exitation eneries. It indeed exhibits the desired flexibility in the sense that the phase-diagram of the model could also be calculated. Further progress towards a new standard for electronic structure calculations of intermediate sized molecules requires several additional developments. We mention two topics: First, the present variant of FRG operates within a static approximation; it would be desirable to explore whether novel concepts, like the ”channel decomposition” that has been used successfully by several other authors, can provide a viable option to go beyond the static limit, so that life-time effects can be dealt with. Second, momentarily FRG calculations are mostly performed for short-range interactions. Quantitative studies of realistic systems will certainly require to include the Coulomb-interaction. Its long range-nature will add to the computational complexity of the matrix equations that are to be solved. To sucessfully deal with all computational challenges so as to harvest the intriguing prospects of FRG as reference tool for electronic structure calculations, it is probably advantantageous to combine efforts and follow this goal within a research consortium. Fortunately, the condensed matter community in Germany is very well set up to achieve this goal in its future research.

Publications

• Density propagator for many-body localization: mobility edges, non-ergodic subdiffusion and stretched exponentials (5 pages, 3 figures)
  S. Bera, G. De Tomasi, F. Weiner, F. Evers
  
• Quasi-Particle Self-Consistent GW for Molecules, J. Comp. Theo. Chem. 12, 5152 (2015)
  F. Kaplan, M. E. Harding, F. Weigend, Chr. Seiler, F. Evers, M. J. van Setten
  
• A functional renormalization group approach to electronic structure calculations for systems without translational symmetry, Phys. Rev. B 94, 155102 (2016)
  Christian Seiler, Ferdinand Evers