  We present a local representation of the electronic dielectric response
function, based on a spatial partition of the dielectric response into
contributions from each Wannier function using a generalized density functional
perturbation theory. This procedure is fully ab initio, and therefore allows us
to rigorously define local metrics, such as "bond polarizability," on Wannier
centers. We show that the locality of the response function is determined by
the locality of three quantities: Wannier functions of the occupied manifold,
the density matrix, and the Hamiltonian matrix. In systems with a gap, the bare
dielectric response is exponentially localized, which supports the physical
picture of the dielectric response function as a collection of interacting
local response that can be captured by a tight-binding model.
