A functional renormalization group approach to electronic structure calculations for systems without translational symmetry

摘要

A formalism for electronic-structure calculations is presented that is basedon the functional renormalization group (FRG). The traditional FRG has beenformulated for systems that exhibit a translational symmetry with an associatedFermi surface, which can provide the organization principle for therenormalization group (RG) procedure. We here advance an alternativeformulation, where the RG-flow is organized in the energy-domain rather than ink-space. This has the advantage that it can also be applied to inhomogeneousmatter lacking a band-structure, such as disordered metals or molecules. Theenergy-domain FRG ({\epsilon}FRG) presented here accounts for Fermi-liquidcorrections to quasi-particle energies and particle-hole excitations. It goesbeyond the state of the art GW-BSE, because in {\epsilon}FRG the Bethe-Salpeterequation (BSE) is solved in a self-consistent manner. An efficientimplementation of the approach that has been tested against exactdiagonalization calculations and calculations based on the density matrixrenormalization group is presented. Similar to the conventional FRG, also the {\epsilon}FRG is able to signalizethe vicinity of an instability of the Fermi-liquid fixed point via runaway flowof the corresponding interaction vertex. Embarking upon this fact, in anapplication of {\epsilon}FRG to the spinless disordered Hubbard model wecalculate its phase-boundary in the plane spanned by the interaction anddisorder strength. Finally, an extension of the approach to finite temperaturesand spin S = 1/2 is also given.