An efficient fluctuation exchange approach to low-temperature spin fluctuations and superconductivity: from the Hubbard model to Na_<i>x</i>CoO_{2 *}<i>y</i>H₂O

Superconductivity arises mostly at energy and temperature scales that are much smaller than the typical bare electronic energies. Since the computational effort of diagrammatic many-body techniques increases with the number of required Matsubara frequencies and thus with the inverse temperature, phase transitions that occur at low temperatures are typically hard to adress numerically. In this work, we implement a fluctuation exchange (FLEX) approach to spin fluctuations and superconductivity using the "intermediate representation basis" (IR) [Shinaoka et al., PRB 96, 2017] for Matsubara Green functions. This FLEX+IR approach is numerically very efficient and enables us to reach temperatures on the order of 10^-4 in units of the electronic band width in multi-orbital systems. After benchmarking the method in the doped repulsive Hubbard model on the square lattice, we study the possibility of spin fluctuation mediated superconductivity in the hydrated sodium cobalte material Na_xCoO_{2 *} yH₂O reaching the scale of the experimental transition temperature T_c = 4.5 K and below.