Green’s function methods for excited states and x-ray spectra of functional materials

Many interesting properties of functional materials, such as dynamic response and thermodynamic behavior, depend on their excited state properties. These functional properties are often related to excitations in the system, such as phonons and plasmons, which lead to inelastic losses, lifetime, and other dynamic effects. The excitations are pure many-body correlation effects that are missing from independent particle theories. They are revealed in x-ray spectra such as photoemission and absorption, where they show up as satellites beyond the quasi-particle approximation. Our main focus in this work is the use of Green’s function methods to describe these effects. In particular, we discuss how the cumulant Green’s function provides a unified treatment of such dynamic correlation effects in many contexts. Besides a robust theoretical framework, these methods also yield widely applicable tools for practical calculations of many functional properties of materials. This methodology is illustrated with a number of applications ranging from optical and x-ray spectra to thermodynamic properties, and dynamic response. Some recent extensions for more correlated systems are also briefly discussed.