Exploring thermal cluster cumulant approaches for the finite temperature electronic structure problem

This paper reviews and explores thermal cluster cumulant approaches for finite temperature electronic structure problems. We examine connections between various formulations and discuss the zero-temperature limit as well as the N-representability problem. Attempts to resolve the N-representability issue are made through the application of positivity constraints. Insights are gained from numerical tests conducted on various model magnetic systems and ab initio molecular systems. For many representative systems the current approach fails to deliver accurate results for thermal electronic structure problems at low temperature.