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

Self-consistent Hartree-Fock approximation combined with solutions of Bethe-Salpeter equation offers a powerful tool

for studies of strong correlation effects arising in condensed matter models, nuclear physics, quantum field theories,

and real materials. The standard finite-T approach would be to first solve the problem in the Matsubara representation

and then apply numerical analytic continuation to the real-frequency axis to link theoretical results

with experimental probes, but this ill-conditioned procedure often distorts important spectral features

even for very accurate imaginary-frequency data. We demonstrate that the ladder-type finite-temperature

Bethe-Salpeter equation in the Hartree-Fock basis for the 3-point vertex function and, ultimately, systems's polarization

can be accurately solved directly on the real frequency axis using the diagrammatic Monte Carlo

technique and series resummation. We illustrate the method by applying it to the homogeneous electron gas model.