Durrant, T. R., Hodgson, M. J. P., Ramsden, J. D., Godby, R. W.
Electron localisation in static and time-dependent one-dimensional model systems
Journal of Physics: Condensed Matter 30, (6),pp 065901/1-6 (2018)
The most direct signature of electron localisation is the tendency of an electron in a many-body system to exclude other same-spin electrons from its vicinity. By applying this concept directly to the exact many-body wavefunction, we find that localisation can vary considerably between different ground-state systems, and can also be strongly disrupted, as a function of time, when a system is driven by an applied electric field. We use this measure to assess the well-known electron localisation function (ELF), both in its approximate single-particle form (often applied within density-functional theory) and its full many-particle form. The full ELF always gives an excellent description of localisation, but the approximate ELF fails in time-dependent situations, even when the exact Kohn-Sham orbitals are employed.