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W. Auzinger, J. Dubois, K. Held, H. Hofstätter, T. Jawecki, A. Kauch, O. Koch, K. Kropielnicka, P. Singh, C. Watzenböck:
"Efficient Magnus-type integrators for solar energy conversion in Hubbard models";
Journal of Computational Mathematics and Data Science (JCMDS), 2 (2022).

Strongly interacting electrons in solids are generically described by Hubbard-type models, and the impact of solar light can be modeled by an additional time-dependence. This yields a finite dimensional system of ordinary differential equations (ODE)s of Schödinger type, which can be solved numerically by exponential time integrators of Magnus type. The efficiency may be enhanced by combining these with operator splittings. We will discuss several different approaches of employing exponential-based methods in conjunction with an adaptive Lanczos method for the evaluation of matrix exponentials and compare their accuracy and efficiency. For each integrator, we use defect-based local error estimators to enable adaptive time-stepping.
This serves to reliably control the approximation error and reduce the computational effort.

Numerical time integration, Magnus-type methods, splitting schemes, Hubbard model

http://dx.doi.org/10.1016/j.jcmds.2021.100018

https://publik.tuwien.ac.at/files/publik_299200.pdf