Computing local multipoint correlators using the numerical\n renormalization group

Abstract

Local three- and four-point correlators yield important insight into strongly\ncorrelated systems and have many applications. However, the nonperturbative,\naccurate computation of multipoint correlators is challenging, particularly in\nthe real-frequency domain for systems at low temperatures. In the accompanying\npaper, we introduce generalized spectral representations for multipoint\ncorrelators. Here, we develop a numerical renormalization group (NRG) approach,\ncapable of efficiently evaluating these spectral representations, to compute\nlocal three- and four-point correlators of quantum impurity models. The key\nobjects in our scheme are partial spectral functions, encoding the system's\ndynamical information. Their computation via NRG allows us to simultaneously\nresolve various multiparticle excitations down to the lowest energies. By\nsubsequently convolving the partial spectral functions with appropriate\nkernels, we obtain multipoint correlators in the imaginary-frequency Matsubara,\nthe real-frequency zero-temperature, and the real-frequency Keldysh formalisms.\nWe present exemplary results for the connected four-point correlators of the\nAnderson impurity model, and for resonant inelastic x-ray scattering (RIXS)\nspectra of related impurity models. Our method can treat temperatures and\nfrequencies -- imaginary or real -- of all magnitudes, from large to\narbitrarily small ones.\n