Efficient fluctuation-exchange approach to low-temperature spin fluctuations and superconductivity: From the Hubbard model to NaxCoO2⋅ yH2O

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 address 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., Phys. Rev. B 96, 035147 (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 bandwidth in multiorbital 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 cobalt material NaxCoO2⋅ yH2O reaching the scale of the experimental transition temperature Tc = 4.5 K and below.