Functional renormalization group approach to electronic structure calculations for systems without translational symmetry
Christian Seiler, Ferdinand Evers
Good progress has been made in electronic structure calculations for real materials as well as for model Hamiltonians. However with an eye on $a\phantom{\rule{0}{0ex}}b$ $i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o$ calculations, it is still very challenging to accurately calculate, e.g., the dynamical response of small molecules or atom clusters. At present the method of choice is the GW-BSE method. Its notorious drawback is that solving a computationally demanding self-consistency equation is required. Thus motivated, the author explore an alternative idea replacing the self-consistency problem by the functional renormalization group (FRG). The traditional FRG was formulated for systems with translational symmetry. We investigate an alternative ($\ensuremath{\epsilon}$FRG) that is also applicable to inhomogeneous matter, such as disordered metals or molecules. It accounts for Fermi-liquid corrections to quasiparticle energies and particle-hole excitations. In principle it can go beyond the state of the art approximation, GW-BSE, by solving the Bethe-Salpeter equation (BSE) self-consistently We present an efficient implementation of $\ensuremath{\epsilon}$FRG together with performance tests on the spinless disordered Hubbard model.
arXiv:1605.07024•Physical review. B./Physical review. B•Oct 3, 2016•2 citations