Speaker
Description
The many-body problem is usually approached from one of two perspectives: the first originates from an action and is based on Feynman diagrams, the second is centered around a Hamiltonian and deals with quantum states and operators. The connection between results obtained in either way is made through spectral (or Lehmann) representations, well known for two-point correlators. We have derived generalized spectral representations for multipoint correlators that complete this picture and apply in the imaginary-frequency Matsubara, the real-frequency zero-temperature, and the real-frequency Keldysh formalisms. Our spectral representations consist of partial spectral functions, containing the system-specific information, and convolution kernels, encoding the formalism-dependent time-ordering prescription, and thereby elucidate the relation between the different many-body formalisms.
In this talk, I will first describe how we derive the generalized spectral representations and what they tell us about analytic properties of multipoint correlators. Then, I will present numerical results for the four-point vertex of the Anderson impurity model and the DMFT solution of the Hubbard model, discussing imaginary-frequency Matsubara and real-frequency Keldysh data. The numerical results are obtained using our numerical renormalization group (NRG) scheme explained in the opening talk by Jan von Delft.
