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We present a finite-temperature extension of the retarded cumulant Green'sfunction for calculations of exited-state and thermodynamic properties ofelectronic systems. The method incorporates a cumulant to leading order in thescreened Coulomb interaction $W$ and improves excited state properties comparedto the $GW$ approximation of many-body perturbation theory. Results for thehomogeneous electron gas are presented for a wide range of densities andtemperatures, from cool to warm dense matter regime, which reveal severalhitherto unexpected properties. For example, correlation effects remain strongat high $T$ while the exchange-correlation energy becomes small. In addition,the spectral function broadens and damping increases with temperature, blurringthe usual quasi-particle picture. Similarly Compton scattering exhibitssubstantial many-body corrections that persist at normal densities andintermediate $T$. Results for exchange-correlation energies and potentials arein good agreement with existing theories and finite-temperature DFTfunctionals.

Finite temperature Green's function approach for excited state and thermodynamic properties of cool to warm dense matter