Local three- and four-point correlators yield important insight into strongly correlated systems and have many applications. However, the nonperturbative, accurate computation of dynamical multipoint correlators is challenging, particularly in the real-frequency domain for systems at low temperatures. We have developed generalized spectral representations for multipoint correlators, and a numerical renormalization group (NRG) approach for computing local three- and four-point correlators of quantum impurity models. The key ingredients in our scheme are partial spectral functions, encoding the system’s dynamical information. Their computation via NRG allows us to simultaneously resolve various multiparticle excitations down to the lowest energies. By subsequently convolving the partial spectral functions with appropriate kernels, we obtain multipoint correlators in the imaginary-frequency Matsubara, the real-frequency zero-temperature, and the real-frequency Keldysh formalisms.
In this talk, I will begin with a review of the NRG computation of real-frequency two-point spectral functions and correlators and discuss some examples involving DMFT+NRG applications. I will then describe how the NRG methodology can be generalized from two-point to three- and four-point spectral functions, and present exemplary results for the connected four-point correlators of the Anderson impurity model.
In a subsequent talk, Fabian Kugler will discuss the generalized spectral representations for multipoint correlators in detail and show additional numerical results for the four-point vertex obtained using our scheme.