Multipoint Correlation Functions: Spectral Representation and Numerical Evaluation

One-particle (or two-point) correlation functions have a well-known Lehmann representation, revealing the relation between their real- and imaginary-frequency variants, and can be computed by several means. For two-particle (or four-point) functions, an analogous representation and non-perturbative numerical results were previously known for imaginary frequencies only, and results on the real-frequency axis largely remained elusive. Here, we present spectral representations for multipoint correlation functions for each of three widely-used formalisms: the zero-temperature, Matsubara, and Keldysh formalisms. The spectral representations separate information on the system's dynamics, encoded in universal partial spectral functions, from the correlators' analytical properties, encoded in formalism-dependent convolution kernels. Using a novel numerical renormalization group scheme, we compute results for the four-point vertex of the Anderson impurity model. Starting with the Matsubara formalism, our approach allows us to obtain results at arbitrarily low temperatures. Continuing with the Keldysh formalism, we consider the dynamical mean-field solution of the Hubbard model and discuss the rich real-frequency structure of the vertex in the metal-insulator coexistence regime.

Multipoint Correlation Functions: Spectral Representation and Numerical Evaluation

F. B. Kugler, S.-S. B. Lee and J. von Delft Phys. Rev. X 11, 041006 (2021).

https://link.aps.org/doi/10.1103/PhysRevX.11.041006

Computing Local Multipoint Correlators Using the Numerical Renormalization Group S.-S. B. Lee, F. B. Kugler and J. von Delft Phys. Rev. X 11, 041007 (2021).

https://link.aps.org/doi/10.1103/PhysRevX.11.041007