A Chebychev propagator with iterative time ordering for explicitly time-dependent Hamiltonians

TL;DR

This paper introduces an iterative Chebychev propagator for solving explicitly time-dependent Schrödinger equations, improving accuracy and efficiency by effectively handling time ordering through an iterative approach.

Contribution

It presents a novel iterative Chebychev propagator that accurately and efficiently incorporates time ordering in explicitly time-dependent quantum dynamics.

Findings

Robust and accurate propagation method demonstrated.

Outperforms existing schemes in efficiency and accuracy.

Effective handling of time ordering in quantum simulations.

Abstract

A propagation method for time-dependent Schr\"odinger equations with an explicitly time-dependent Hamiltonian is developed where time ordering is achieved iteratively. The explicit time-dependence of the time-dependent Schr\"odinger equation is rewritten as an inhomogeneous term. At each step of the iteration, the resulting inhomogeneous Schr\"odinger equation is solved with the Chebychev propagation scheme presented in J. Chem. Phys. 130, 124108 (2009). The iteratively time-ordering Chebychev propagator is shown to be robust, efficient and accurate and compares very favorably to all other available propagation schemes.