Efficient Magnus-type integrators for solar energy conversion in Hubbard models

Abstract

Strongly interacting electrons in solids are generically described by Hubbardtype 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 Schrödinger 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.

Photoexcitations in the Hubbard model -- generalized Loschmidt amplitude analysis of impact ionization in small clusters

“…We presented the analysis of the dynamics of small Hubbard clusters during and after a photoexcitation with a strong electric pulse, focusing on 12-site systems with and wihtout impact ionization. To this end we applied novel commutator free Magnus integrators [25] for the time evolution (solution of the time-dependent Schrödinger equation).…”

“…using optimized commutator-free Magnus integrators of fourth order described in detail as CF4oH in Ref. [25]. As an error tolerance for the adaptive time-stepping algorithm we used tol < 10 −6 .…”