Abstract

Many-body phenomena such quantum criticality, non-Fermi liquid behavior, and perhaps most importantly, unconventional superconductivity, have largely stayed within the province of model theories. But models must rely on educated guesses for their form, and the means of discriminating between model assumptions is limited. As a result the field has remained without a firm foundation for decades. A key reason is that multiple energy scales are operative: the high energy scales that control the low-energy fluctuations cannot be integrated out without model assumptions. Ab initio methods could in principle supplant model Hamiltonians; however, these low-energy phenomena cannot be reliably explained unless both one-particle and two-particle response functions are described with very high fidelity. Limitations to their fidelity has largely precluded them from realizing this possibility. To manage electron correlations, Green’s function methods have proven to be powerful tools in the theorist’s toolbox. Ab initio Green’s function methods have traditionally divided into two tracks: low-order many-body perturbation theory (MBPT), applicable to systems with weak or moderate correlations, and where the independent particle picture is no longer adequate, nonperturbative Dynamical Mean Field Theory (DMFT), added to density functional theory. Each has advantages, but also limitations. In this talk I show recent progress in joining MBPT with DMFT to characterize one- and two-particle spectral functions with much higher fidelity than either separately. In many correlated materials including most unconventional superconductors, spin fluctuations drive low-energy correlations that give rise to exotic phenomena. MBPT , and augmenting it with DMFT when needed, yield a broadly applicable frame- work for electronic structure that describe spectral functions of many kinds of systems with high fidelity. This talk focuses on several unconventional superconductors where MBPT and DMFT must be combined. It shows the promise of these new methods as reliable predictors of unconventional superconductivity, and a basis to identify the dominant mechanisms in a manner that is not possible with models.