Cumulant Green’s function methods for excited state properties of functional materials*

Many interesting properties of functional materials depend on their excited state properties, such as dynamic response and thermodynamic behavior. Often this behavior depends on details of excitations in the system such as phonons and plasmons, which lead to inelastic losses and damping effects. These excitations can be probed by photoemission spectra, where they show up as satellites beyond the quasi-particle peak [1]. These many-body effects are neither amenable to density functional theory nor extensions based on quasi-particle approximations. Here we discuss an approach based on the cumulant Green’s function, which provides a unified treatment of such dynamic correlation effects [2]. The approach is illustrated with several applications. Remarkably, a cumulant calculated in linear response within a quasi-boson approximation, is adequate to explain the loss spectra and charge-transfer excitations in many systems. Finite-temperature exchange-correlation potentials, thermodynamic properties, and the finite-temperatureTDDFT kernel, and can also be obtained [3,4]. Finally, some extensions are briefly discussed, including nonlinear contributions to the cumulant [5].
[1] Jianqiang Sky Zhou et al., PNAS, https://doi.org/10.1073/pnas.2012625117.
[2] L. Hedin, J. Phys.: Condens. Matter 11, R489 (1999).
[3] J. J. Kas, et al., Phys. Rev. B 100, 195144 (2019).
[4] John J. Rehr and Joshua J. Kas, Eur. Phys. J. B 91, 153 (2018).
[5] M. Tzavala et al., Phys. Rev. Research 2, 033147 (2020).