Two-particle properties within finite-temperature self-consistent one-particle Green’s function methods: theory and application

Finite-temperature Green’s function methods, such as GF2 and GW, provide a route to model many-body electronic structure of materials at finite temperature. Although these methods give useful thermodynamic quantities, properties are usually limited to the information contained in the one-particle Green’s function, such as one-particle density matrix. We show that two-particle density matrices and two-particle properties can be accessed through application of Hellmann-Feynman theorem, bypassing Bethe-Salpeter equation. The obtained two-particle density matrices provide a useful set of diagnostics for GF2 and GW, closely connecting them with wave-function approaches.