Exchange and correlation effects in finite-temperature TDDFT

We discuss the finite-temperature (FT) generalization of time-dependent density functional theory (TDDFT) [1]. Formally the theory is analogous to that at temperature T = 0. In the local density approximation, the FT exchange-correlation kernel f_xc(T,n) can again be expressed as a density derivative of the exchange correlation potential d v_xc(T,n)/dn, where n = N/V is the electron number density. An approximation for the TDDFT kernel f_xc(T,n) is obtained from the FT generalization of the retarded cumulant expansion applied to the homogeneous electron gas [2]. Results for f_xc and for the FT loss function are shown for a wide range of temperatures and densities, including the warm dense matter regime with temperatures of order T_F , the electron degeneracy temperature. The FT cumulant Green’s function approach also yields a physical interpretation of the exchange and correlation contributions to the theory.
[1] Eur. Phys. J. B 91, 153 (2018).
[2] J.J. Kas, J.J. Rehr, Phys. Rev. Lett. 119, 176403 (2017).