Spectral representation of Matsubara n-point functions: Exact kernel functions and applications

Abstract

In the field of quantum many-body physics, the spectral (or Lehmann) representation simplifies the calculation of Matsubara $n$-point correlation functions if the eigensystem of a Hamiltonian is known. It is expressed via a universal kernel function and a system- and correlator-specific product of matrix elements. Here we provide the kernel functions in full generality, for arbitrary $n$, arbitrary combinations of bosonic or fermionic operators and an arbitrary number of anomalous terms. As an application, we consider bosonic 3- and 4-point correlation functions for the fermionic Hubbard atom and a free spin of length $S$, respectively.