SQUIRREL: An open-source software suite for quantum dynamics calculations on complex geometries with time-dependent electric/magnetic fields

We present a general-purpose, open-source software suite, SQUIRREL (Streamlined Quantum Unified Interface for Researching Real-time Excitations with Light), for propagating the time-dependent Schrödinger equation on complex geometries in the presence of time-dependent electric and/or magnetic fields. To handle large systems that can be executed on a conventional desktop computer, the SQUIRREL software suite uses a suite of efficient propagation methods for various quantum dynamics applications, including a new perturbation-based element-dropping algorithm that improves computational performance with minimal loss of accuracy. We analyze the efficacy of these optimizations for Crank-Nicolson, scaled Taylor series approximation, and split-operator propagation methods and discuss the range of their applicability to a variety of quantum dynamics problems. In addition, we provide several examples of time-dependent dynamics calculations and extensive documentation for generating custom geometries, potentials, and time-propagation approaches. Our numerical benchmarks and results demonstrate the versatility of the SQUIRREL software suite for efficiently calculating quantum dynamics in complex nanoscale geometries, particularly in the presence of time-dependent magnetic fields, which have received less attention in previous quantum dynamics studies.

Program summary

Program Title: SQUIRREL

CPC Library link to program files: https://doi.org/10.17632/kfvs5s88sj.1

Licensing provisions: GNU General Public License 3

Programming language: MATLAB

Supplementary material: Additional details on calculations with an anisotropic effective mass, determination of timesteps, propagation timings, and element-dropping timings.

Nature of problem: The SQUIRREL software suite solves the time-dependent Schrödinger equation for electronic states in the presence of time-dependent electric and/or magnetic fields. The code is well-suited for calculating electron dynamics of complex nanostructures in the effective mass approximation, using various propagation and sparse-matrix techniques to reduce the computational complexity of these problems. The program provides a user-friendly interface for testing these optimizations and generating custom geometries and potentials for systems of interest.

Solution method: The SQUIRREL software suite uses Crank-Nicolson, split-operator, Padé approximant, and scaled-Taylor-series-based propagation methods to calculate electron dynamics on a finite-element basis. The code includes a novel perturbation-based element-dropping method, which enables sparse representations of the typically dense finite element Hamiltonian matrix. This capability enables a highly efficient and flexible approach for calculating driven dynamics in quantum systems with complex geometries and time-dependent electric/magnetic fields.