TY  - JOUR
A1  - Dürrnagel, Matteo
A1  - Beyer, Jacob
A1  - Thomale, Ronny
A1  - Schwemmer, Tilman
T1  - Unconventional superconductivity from weak coupling
JF  - The European Physical Journal B
N2  - We develop a joint formalism and numerical framework for analyzing the superconducting instability of metals from a weak coupling perspective. This encompasses the Kohn–Luttinger formulation of weak coupling renormalization group for superconductivity as well as the random phase approximation imposed on the diagrammatic expansion of the two-particle Green’s function. The central quantity to resolve is the effective interaction in the Cooper channel, for which we develop an optimized numerical framework. Our code is capable of treating generic multi-orbital models in two as well as three spatial dimensions and, in particular, arbitrary avenues of spin-orbit coupling.
KW  - superconducting instability
KW  - metals
KW  - weak coupling
KW  - unconventional superconductivity
Y1  - 2022
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-325153
SN  - 1434-6028
VL  - 95
IS  - 7
ER  - 
TY  - JOUR
A1  - Beyer, Jacob
A1  - Goth, Florian
A1  - Müller, Tobias
T1  - Better integrators for functional renormalization group calculations
JF  - The European Physical Journal B
N2  - We analyze a variety of integration schemes for the momentum space functional renormalization group calculation with the goal of finding an optimized scheme. Using the square lattice t-t' Hubbard model as a testbed we define and benchmark the quality. Most notably we define an error estimate of the solution for the ordinary differential equation circumventing the issues introduced by the divergences at the end of the FRG flow. Using this measure to control for accuracy we find a threefold reduction in number of required integration steps achievable by choice of integrator. We herewith publish a set of recommended choices for the functional renormalization group, shown to decrease the computational cost for FRG calculations and representing a valuable basis for further investigations.
KW  - functional renormalization group
KW  - FRG
KW  - FRG calculations
KW  - integrators
KW  - ordinary differential equations
KW  - ODE
Y1  - 2022
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-325131
SN  - 1434-6028
VL  - 95
IS  - 7
ER  -