Response functions of correlated systems in the linear regime and beyond

Abstract

The technological progress in material science has paved the way to engineer new condensed matter systems. Among those, fascinating properties are found in presence of strong correlations among the electrons. The maze of physical phenomena they exhibit is countered by the difficulty in devising accurate theoretical descriptions. This explains the plethora of approximated theories aiming at the closest reproduction of their properties. In this respect, the response of the system to an external perturbation bridges the experimental evidence with the theoretical description, representing a testing ground to prove or disprove the validity of the latter. In this thesis we develop a number of theoretical and numerical strategies to improve the computation of linear response functions in several of the forefront many-body techniques. In particular, the development of computationally efficient schemes, driven by physical arguments, has allowed (i) improvements in treating the local two-particle correlations and scattering functions, which represent essential building blocks for established non-perturbative theories, such as dynamical mean field theory (DMFT) and its diagrammatic extensions and (ii) the implementation of the groundbreaking multiloop functional renormalization group (mfRG) technique and its application to a two-dimensional Hubbard model. Together with (i), the multiloop scheme has promoted the functional RG to provide quantitative predictions. As the mfRG is able to build up a complete subset of Feynman diagrams, such as those of the parquet approximation, its results are independent on the choice of the cutoff scheme as well as on the way (direct or through a post-processing treatment) response functions are calculated. We demonstrate by hand of precise numerical calculations that both properties are fulfilled by a satisfactory degree of accuracy. We also elaborate how these properties could be exploited in the future for improving the numerical solution of parquet-based algorithms. Finally, our study reveals that an important piece of physical information can be accessed by looking at the nonlinear response of the system to an external field. In particular, a DMFT study of the pairing response function to a superconducting probe beyond the linear regime, has pinpointed a simple criterion to identify the presence of a preformed pair phase. This result provides a complementary information to cutting-edge theoretical approaches and, possibly, to non-equilibrium experiments, to shed some light on the nature of the pseudogap in high-Tc superconductors.