A functional renormalization group approach to electronic structure calculations for systems without translational symmetry
arXiv:1605.07024 · doi:10.1103/PhysRevB.94.155102
Abstract
A formalism for electronic-structure calculations is presented that is based on the functional renormalization group (FRG). The traditional FRG has been formulated for systems that exhibit a translational symmetry with an associated Fermi surface, which can provide the organization principle for the renormalization group (RG) procedure. We here advance an alternative formulation, where the RG-flow is organized in the energy-domain rather than in k-space. This has the advantage that it can also be applied to inhomogeneous matter lacking a band-structure, such as disordered metals or molecules. The energy-domain FRG (εFRG) presented here accounts for Fermi-liquid corrections to quasi-particle energies and particle-hole excitations. It goes beyond the state of the art GW-BSE, because in εFRG the Bethe-Salpeter equation (BSE) is solved in a self-consistent manner. An efficient implementation of the approach that has been tested against exact diagonalization calculations and calculations based on the density matrix renormalization group is presented. Similar to the conventional FRG, also the εFRG is able to signalize the vicinity of an instability of the Fermi-liquid fixed point via runaway flow of the corresponding interaction vertex. Embarking upon this fact, in an application of εFRG to the spinless disordered Hubbard model we calculate its phase-boundary in the plane spanned by the interaction and disorder strength. Finally, an extension of the approach to finite temperatures and spin S = 1/2 is also given.
25 pages, 14 figures
References in corpus (20)
- Many body localization and thermalization in quantum statistical mechanics
- Anderson Transitions
- Quasiparticle self-consistent method; a basis for the independent-particle approximation
- Efficient implementation of the GW approximation within the all-electron FLAPW method
- Quasi-Particle Self-Consistent for Molecules
- A finite-frequency functional RG approach to the single impurity Anderson model
- Equation of state of the two-dimensional Hubbard model
- Impurity and correlation effects on transport in one-dimensional quantum wires
- Renormalized mean-field analysis of antiferromagnetism and d-wave superconductivity in the two-dimensional Hubbard model
- Functional renormalization group for Luttinger liquids with impurities
- Renormalization-group analysis of the one-dimensional extended Hubbard model with a single impurity
- Fermionic two-loop functional renormalization group for correlated fermions: Method and application to the attractive Hubbard model
- Superconductivity in the attractive Hubbard model: functional renormalization group analysis
- Metal-insulator transition from combined disorder and interaction effects in Hubbard-like electronic lattice models with random hopping
- The two-loop functional renormalization-group approach to the one- and two-dimensional Hubbard model
- Quantum criticality of reconstructing Fermi surfaces in antiferromagnetic metals
- Fermionic renormalization group methods for transport through inhomogeneous Luttinger liquids
- Low-energy effective interactions beyond the constrained random-phase approximation by the functional renormalization group
- Non-Fermi-liquid behavior and anomalous suppression of Landau damping in layered metals close to ferromagnetism
- Effects of non-magnetic impurities on spin-fluctuations induced superconductivity