Uplifting Green's function methods

Approximating the one-body Green’s function beyond the GW level remains a central challenge in many-body theory. Moreover, higher-order correlators, particularly the two-body Green’s function, are crucial for non-equilibrium approaches, such as the Real-time Dyson Expansion (RT-DE) and the G1-G2 scheme. Recent work [1,2] has introduced a hierarchy of Dyson equations that couple Green’s functions of odd (even) particle order to time-contracted even (odd) higher-order correlators, providing a systematic route to include correlations beyond GW.

In this work we explore uplifting approaches, where lower-order Green’s functions are embedded in higher-order ones, to enable physically guided approximations at the level of multi-particle correlators. Using exact-diagonalization results for a long-range, multi-band Hubbard model, we illustrate the exact structure of the higher-order correlators and analyze multi-particle excitation signatures in the photoemission spectrum of the one-body Green’s function. Finally, we discuss how this framework may serve as a foundation for incorporating exciton–exciton and other multi-particle interactions directly into two-body Green’s function.

[1] G. Riva, P. Romaniello, J Arjan Berger, Phys. Rev. Lett. 131, 216401 (2023)

[2] G. Riva et al, Phys. Rev. B 111, 195133 (2025)