Seung-Sup Lee (University of Munich, Germany): Multipoint correlation functions: spectral representation and numerical evaluation

Four-point correlation functions on the real-frequency axis describe experimentally relevant properties, such as nonlocal susceptibilities and vertex corrections to conductivity, of the systems of interacting quantum particles. However, the nonperturbative computation of real-frequency multipoint functions has been intractable. In this talk, I will summarize our recently developed method for computing multipoint functions and its applications [1, 2]. We have derived generalized spectral representations for multipoint functions that apply in all of the commonly used many-body frameworks [1]: the imaginary-frequency Matsubara and the real-frequency zero-temperature and Keldysh formalisms. We have developed a numerical renormalization group (NRG) method for evaluating the spectral representations for local multipoint functions, which can treat temperatures and frequencies---imaginary or real---of all magnitudes, from large to arbitrarily small ones [2]. I will present the numerical results of four-point vertex functions and resonant inelastic x-ray scattering (RIXS) spectra of quantum impurity systems. [1] F. B. Kugler, S.-S. B. Lee, and J. von Delft, arXiv:2101.00707 [2] S.-S. B. Lee, F. B. Kugler, and J. von Delft, arXiv:2101.00708