Stochastic many-body methods for quasiparticle excitations in realistic nanoscale systems

I will present recent developments in predicting electronic excitations using the combination of stochastic computational techniques and many-body theory. The methodology relies on operators' decomposition via random vectors and recasting expectation values as statistical estimators.
In practice, the implementation of diagrammatic methods employs real-time and real-space sampling.[1] This formalism leads to substantial computational savings and reduced scaling with the number of electrons; it enables first-principles predictions of quasiparticle energies in systems with thousands of atoms. In detail, I will describe our recent work on simulating nanoscale condensed systems within the linear scaling stochastic GW approximation.[2,3,4] Further, I will show that statistical sampling of interactions is an efficient route to go beyond GW: I will detail our work on the stochastic GWΓ approach, which combines non-local vertex corrections in the screened Coulomb interaction and self-energy.[5] I will demonstrate that the vertex corrections affect unoccupied states, improve the quasiparticle energies, and capture multi-quasiparticle excitations otherwise missing in GW.[5,6] Despite the increased complexity of the self-energy, the stochastic GWΓ scales linearly with the system size.

[1] V Vlcek, W Li, R Baer, E Rabani, D Neuhauser, Physical Review B 98 (7), 075107 (2018)
[2] J Brooks, G Weng, S Taylor, V Vlcek, Journal of Physics: Condensed Matter 32 (23), 234001 (2020)
[3] G Weng, V Vlcek The Journal of Physical Chemistry Letters 11 (17), 7177-7183 (2020)
[4] M Romanova, V Vlcek The Journal of Chemical Physics 153 (13), 134103 (2020)
[5] V Vlcek, Journal of Chemical Theory and Computation 15 (11), 6254-6266 (2019)
[6] C Mejuto-Zaera, et al., arXiv preprint arXiv:2009.0240122020