  Diagrammatic expansions are a central tool for treating correlated electron
systems. At thermal equilibrium, they are most naturally defined within the
Matsubara formalism. However, extracting any dynamic response function from a
Matsubara calculation ultimately requires the ill-defined analytical
continuation from the imaginary- to the real-frequency domain. It was recently
proposed [Phys. Rev. B 99, 035120 (2019)] that the internal Matsubara
summations of any interaction-expansion diagram can be performed analytically
by using symbolic algebra algorithms. The result of the summations is then an
analytical function of the complex frequency rather than Matsubara frequency.
Here we apply this principle and develop a diagrammatic Monte Carlo technique
which yields results directly on the real-frequency axis. We present results
for the self-energy $\Sigma(\omega)$ of the doped 32x32 cyclic square-lattice
Hubbard model in a non-trivial parameter regime, where signatures of the
pseudogap appear close to the antinode. We discuss the behavior of the
perturbation series on the real-frequency axis and in particular show that one
must be very careful when using the maximum entropy method on truncated
perturbation series. Our approach holds great promise for future application in
cases when analytical continuation is difficult and moderate-order perturbation
theory may be sufficient to converge the result.

Strongly Correlated Electrons