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

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.