On the use of Neumann's principle for the calculation of the polarizability tensor of nanostructures

TL;DR

This paper discusses how symmetry considerations, based on Neumann's principle, can optimize the computational calculation of the polarizability tensor in nanostructures, reducing the number of necessary simulations.

Contribution

It introduces a symmetry-based approach leveraging Neumann's principle to efficiently compute the polarizability tensor, minimizing computational effort.

Findings

Symmetry considerations can reduce calculation complexity.

Application demonstrated with real space and spin space symmetries.

Method applicable to electrical and spin response calculations.

Abstract

The polarizability measures how the system responds to an applied electrical field. Computationally, there are many different ways to evaluate this tensorial quantity, some of which rely on the explicit use of the external perturbation and require several individual calculations to obtain the full tensor. In this work, we present some considerations about symmetry that allow us to take full advantage of Neumann's principle and decrease the number of calculations required by these methods. We illustrate the approach with two examples, the use of the symmetries in real space and in spin space in the calculation of the electrical or the spin response.