Adaptive propagation of quantum few-body systems with time-dependent Hamiltonians

TL;DR

This paper compares various numerical methods for solving the time-dependent Schrödinger equation in few-body quantum systems, proposing an adaptive exponential integrator that improves efficiency and accuracy over existing techniques.

Contribution

It introduces an adaptive exponential integrator method tailored for time-dependent quantum systems, enhancing computational efficiency and accuracy.

Findings

The proposed method outperforms other tested methods in speed.

Adaptive time-stepping improves solution accuracy.

The approach is effective for large basis size systems.

Abstract

In this study, a variety of methods are tested and compared for the numerical solution of the Schr\"odinger equation for few-body systems with explicitely time-dependent Hamiltonians, with the aim to find the optimal one. The configuration interaction method, generally applied to find stationary eigenstates accurately and without approximations to the wavefunction's structure, may also be used for the time-evolution, which results in a large linear system of ordinary differential equations. The large basis sizes typically present when the configuration interaction method is used calls for efficient methods for the time evolution. Apart from efficiency, adaptivity (in the time domain) is the other main focus in this study, such that the time step is adjusted automatically given some requested accuracy. A method is suggested here, based on an exponential integrator approach, combined with different ways to implement the adaptivity, which was found to be faster than a broad variety of other methods that were also considered.