Exponential propagators for the Schrödinger equation with a time-dependent potential
This work provides more efficient numerical integration methods for quantum dynamics simulations, benefiting computational physics and chemistry.
The paper develops new commutator-free exponential propagators for the Schrödinger equation with time-dependent potentials, achieving fourth- and sixth-order accuracy with reduced computational cost. Numerical examples demonstrate improved efficiency over existing methods.
We consider the numerical integration of the Schrödinger equation with a time-dependent Hamiltonian given as the sum of the kinetic energy and a time-dependent potential. Commutator-free (CF) propagators are exponential propagators that have shown to be highly efficient for general time-dependent Hamiltonians. We propose new CF propagators that are tailored for Hamiltonians of said structure, showing a considerably improved performance. We obtain new fourth- and sixth-order CF propagators as well as a novel sixth-order propagator that incorporates a double commutator that only depends on coordinates, so this term can be considered as cost-free. The algorithms require the computation of the action of exponentials on a vector similarly to the well known exponential midpoint propagator, and this is carried out using the Lanczos method. We illustrate the performance of the new methods on several numerical examples.