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Self-consistent Hartree-Fock approximation combined with solutions ofBethe-Salpeter equation offers a powerful tool for studies of strongcorrelation effects arising in condensed matter models, nuclear physics,quantum field theories, and real materials. The standard finite-temperatureapproach would be to first solve the problem in the Matsubara representationand then apply numerical analytic continuation to the real-frequency axis tolink theoretical results with experimental probes, but this ill-conditionedprocedure often distorts important spectral features even for very accurateimaginary-frequency data. We demonstrate that the ladder-typefinite-temperature Bethe-Salpeter equation in the Hartree-Fock basis for the3-point vertex function and, ultimately, system's polarization can beaccurately solved directly on the real frequency axis using the diagrammaticMonte Carlo technique and series resummation. We illustrate the method byapplying it to the homogeneous electron gas model and demonstrate how multiplescattering events renormalize Landau damping.

Solving the Bethe-Salpeter Equation in Real Frequencies at Finite Temperature