Real-frequency responses at finite temperature: Electron gas

To connect finite-temperature calculations with experimental probes not based on thermodynamic potentials, one needs to compute response functions (or spectral densities) at real frequencies. The notorious problem faced by simulations performed in the Matsubara representation is a need for a numerical analytic continuation (NAC) procedure from the imaginary to the real-frequency domain because even if the Matsubara data are known with high accuracy, the NAC will fail to correctly reproduce complex spectra. Here we show that the Diagrammatic Monte Carlo technique allows one to compute finite-temperature response functions directly on the real-frequency axis within any field-theoretical formulation of the interacting fermion problem. There are no limitations on the type and nature of the system's action or whether partial summation and self-consistent treatment of certain diagram classes are used. In particular, by eliminating the need for numerical analytic continuation from a Matsubara representation, our scheme allows to study spectral densities of arbitrary complexity with controlled accuracy in models with frequency-dependent effective interactions. The feasibility of the method is demonstrated by considering the problem of the plasmon line-width in a homogeneous electron gas.