Real-Frequency Response Functions at Finite Temperature

Building on previous developments [A. Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlanc, Phys. Rev. B 99, 035120 (2019); PRBMDO2469-995010.1103/PhysRevB.99.035120A. Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlancPhys. Rev. B101, 125109 (2020); PRBMDO2469-995010.1103/PhysRevB.101.125109A. Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlancPhys. Rev. B102, 045115 (2020)PRBMDO2469-995010.1103/PhysRevB.102.045115, B. Holm and U. von Barth, Phys. Rev. B 57, 2108 (1998)PRBMDO0163-182910.1103/PhysRevB.57.2108, J. Vičičević and M. Ferrero, Phys. Rev. B 101, 075113 (2020)PRBMDO2469-995010.1103/PhysRevB.101.075113], we show that the diagrammatic Monte Carlo technique allows us 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 us to study spectral densities of arbitrary complexity with controlled accuracy in models with frequency-dependent effective interactions. For illustrative purposes we consider the problem of the plasmon linewidth in a homogeneous electron gas (jellium).