A Local Representation Of The Dielectric Response Function

The screened dielectric response function ($\\chi$) is a fundamental physical quantity that captures the many-electron correlation effect, key to a range of excited state properties formulated in the GW/BSE framework. Although $\\chi$ is non-local by definition, a real space partition of $\\chi$ onto local structural motifs can help us gain further physical insight into, e.g., effective local screening properties. Because the bare response function, $\\chi_0$, is normally expressed in electron hole pairs, standard localization procedures for electron wave functions can not be directly applied. In this work, we propose a new method to decompose $\\chi_0$ and $\\chi$ into contributions from local response of Wannier orbitals. We demonstrate that the localization properties of the local response can be exploited to build a local basis set for the dielectric response function, which can be used to construct a tight-binding Hamiltonian to perform dielectric band structure interpolation.