Examining correlation via a temperature- and density-dependent mixing parameter for hybrid density functional approximations

A finite-temperature extension of the two-legged adiabatic connection construction is demonstrated for the uniform electron gas and asymmetric Hubbard dimer, providing the structure of a temperature- and density-dependent weighting scheme for a hybrid exchange-correlation approximation. The construction shows that nonlinear thermal effects on the balance between exchange and correlation, as well as that between correlation components, persist and can even be emphasized by strong electron-electron interaction. These findings point additionally to a complicated interplay between temperature, density, and interaction strength in the strong correlation character of these model systems and provide a new approach to analyzing exchange-correlation entropy.