Computing Local Multipoint Correlators Using the Numerical Renormalization Group

Local three- and four-point correlators yield important insight into strongly correlated systems and have many applications. However, the nonperturbative, accurate computation of multipoint correlators is challenging, particularly in the real-frequency domain for systems at low temperatures. In the accompanying paper, we introduce generalized spectral representations for multipoint correlators. Here, we develop a numerical renormalization group approach, capable of efficiently evaluating these spectral representations, to compute local three- and four-point correlators of quantum impurity models. The key objects in our scheme are partial spectral functions, encoding the system's dynamical information. Their computation via numerical renormalization group 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 realfrequency zero-temperature, and the real-frequency Keldysh formalisms. We present exemplary results for the connected four-point correlators of the Anderson impurity model, and for resonant inelastic x-ray scattering spectra of related impurity models. Our method can treat temperatures and frequenciesimaginary or real-of all magnitudes, from large to arbitrarily small ones.

Automated summary

Local three- and four-point correlators play a crucial role in understanding strongly correlated systems, and a new numerical renormalization group approach is introduced to efficiently compute them, providing insights into multiple particle excitations even at the lowest energies. Exemplary results demonstrate the method's versatility in handling a wide range of temperatures and frequencies, from large to arbitrarily small ones.